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Page 1: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3
Page 2: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

11) 12v2 ⋅ 6v2 12) 8b3

⋅ 10b

13) 15n3 ⋅ 15n3 14) 10x ⋅ 6x

15) 6a2 ⋅ 6a2

16) 6n2 ⋅ 3n2

17) 6x3 ⋅ 3x 18) 8x2

⋅ 10x3

19) 5 p3 ⋅ 20p2 20) 3m3

⋅ 5m

2

Page 3: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

21) 2n ⋅ 3n2 22) 6x ⋅ 10x

23) 3b3 ⋅ 2b 24) 2n ⋅ 2n3

25) 6x3 ⋅ 2x 26) 3x ⋅ 2x2

27) 8k ⋅ 8k328) 8a2

⋅ 8a2

29) 8x2 ⋅ 3x3 30) 15x2

⋅ 6x3

3

Page 4: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

31) 12m3 ⋅ 3m 32) 6 p ⋅ 2p

33) 2n3 ⋅ 2n3 34) 8r3

⋅ 6r3

35) 12x3 ⋅ 5x2

36) 5n2 ⋅ 15n

37) 2x ⋅ 5x338) 10b ⋅ 2b3

39) 5v2 ⋅ 10v3 40) 2a2

⋅ 2a2

4

Page 5: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

41) 2k3 ⋅ 3k2 42) 3x2

⋅ 2x

43) 10x2 ⋅ 2x 44) 2n3

⋅ 10n2

45) 2m ⋅ 2m 46) 6 p3 ⋅ 8p3

47) 2n3 ⋅ 8n 48) 6x2

⋅ 2x

49) 3r3 ⋅ 16r3 50) 12b ⋅ 3b2

5

Page 6: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

51) 20a2 ⋅ 15a2 52) 3x ⋅ 6x3

53) 15v2 ⋅ 12v2 54) 25x ⋅ 10x3

55) 25a2 ⋅ 5a 56) 10x2

⋅ 10x

57) 6 p3 ⋅ 2p2

58) 5n ⋅ 10n3

59) 2m3 ⋅ 2m 60) 3r2

⋅ 2r3

6

Page 7: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

61) 2n ⋅ 6n 62) 3b ⋅ 2b3

63) 8x2 ⋅ 5x2 64) 2v2

⋅ 8v

65) 3n3 ⋅ 3n2

66) 20x2 ⋅ 20x

67) 20k ⋅ 15k 68) 6x ⋅ 6x

69) 10x2 ⋅ 12x3 70) 8n3

⋅ 8n

7

Page 8: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

71) 12m2 ⋅ 12m 72) 10n3

⋅ 10n3

73) 15 p3 ⋅ 10p 74) 4b2

⋅ 4b2

75) 3x2 ⋅ 4x2

76) 5r2 ⋅ 12r

77) 8a2 ⋅ 2a2

78) 15n3 ⋅ 12n

79) 3v ⋅ 9v 80) 15x2 ⋅ 3x3

8

Page 9: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

81) 2k3 ⋅ 3k 82) 10a ⋅ 2a2

83) 12 p3 ⋅ 2p 84) 6n3

⋅ 6n

85) 15x ⋅ 6x386) 10r ⋅ 5r2

87) 2n ⋅ 8n 88) 15b ⋅ 10b3

89) 2m2 ⋅ 6m 90) 3n2

⋅ 3n2

9

Page 10: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

91) 8v2 ⋅ 12v3 92) 15x3

⋅ 5x3

93) 20a ⋅ 10a2 94) 8k3 ⋅ 2k2

95) 4x ⋅ 20x 96) 12n3 ⋅ 5n3

97) 10 p3 ⋅ 2p3

98) 12m2 ⋅ 15m2

99) 15x3 ⋅ 12x2 100) 20b3

⋅ 12b2

10

Page 11: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

101) 12r3 ⋅ 12r2 102) 8x ⋅ 3x3

103) 20n ⋅ 30n 104) 5x2 ⋅ 42x

105) 21a ⋅ 18a3106) 18x ⋅ 10x2

107) 24n2 ⋅ 5n2

108) 21v3 ⋅ 27v2

109) 4k ⋅ 8k 110) 8 p3 ⋅ 6p3

11

Page 12: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

111) 12n ⋅ 12n2 112) 30m3 ⋅ 42m2

113) 6r ⋅ 7r2 114) 35x3 ⋅ 5x

115) 2x2 ⋅ 8x3

116) 24n2 ⋅ 3n3

117) 54v2 ⋅ 54v3

118) 63b ⋅ 35b3

119) 12x ⋅ 21x 120) 12a ⋅ 24a3

12

Page 13: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

121) 28k3 ⋅ 21k3 122) 6n3

⋅ 7n

123) 42 p3 ⋅ 12p3 124) 30m3

⋅ 48m2

125) 12n ⋅ 56n3126) 54x2

⋅ 54x

127) 54 p ⋅ 48p 128) 12n2 ⋅ 6n2

129) 6x3 ⋅ 18x3 130) 40b2

⋅ 27b3

13

Page 14: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

131) 10r ⋅ 24r2 132) 21x2 ⋅ 54x3

133) 15n3 ⋅ 6n 134) 6a ⋅ 3a

135) 24v3 ⋅ 12v3

136) 27x ⋅ 3x3

137) 24x2 ⋅ 21x 138) 12n ⋅ 7n3

139) 21k3 ⋅ 10k2 140) 18 p2

⋅ 8p

14

Page 15: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

141) 5n3 ⋅ 6n 142) 6r ⋅ 3r2

143) 10m2 ⋅ 18m 144) 6x ⋅ 6x2

145) 45n2 ⋅ 20n2

146) 5v ⋅ 25v2

147) 18x ⋅ 10x3148) 63b3

⋅ 35b2

149) 6x3 ⋅ 42x 150) 12n ⋅ 42n

15

Page 16: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

151) 14k2 ⋅ 8k 152) 35x3

⋅ 12x2

153) 30a3 ⋅ 12a3 154) 14 p ⋅ 10p3

155) 49n2 ⋅ 63n 156) 30m ⋅ 30m3

157) 5n2 ⋅ 45n2

158) 48r ⋅ 24r2

159) 10b ⋅ 15b 160) 10x ⋅ 18x2

16

Page 17: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

161) 42r3 ⋅ 27r3 162) 15n ⋅ 30n3

163) 45x2 ⋅ 28x2 164) 30a3

⋅ 20a2

165) 6x ⋅ 24x 166) 35x3 ⋅ 15x3

167) 27n3 ⋅ 24n2

168) 18k ⋅ 24k3

169) 10 p3 ⋅ 15p 170) 28x ⋅ 63x

17

Page 18: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

171) 10m2 ⋅ 8m 172) 12r ⋅ 14r2

173) 7x2 ⋅ 7x 174) 40n3

⋅ 30n

175) 28b3 ⋅ 12b 176) 8v2

⋅ 72v3

177) 12x ⋅ 3x 178) 6n3 ⋅ 2n

179) 42k2 ⋅ 24k3 180) 21a2

⋅ 6a3

18

Page 19: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

181) 24x2 ⋅ 6x2 182) 20 p ⋅ 30p2

183) 42n ⋅ 15n 184) 42m3 ⋅ 72m2

185) 12n2 ⋅ 30n3

186) 12b ⋅ 48b2

187) 56r ⋅ 63r3188) 54x3

⋅ 12x2

189) 35n2 ⋅ 35n3 190) 25a ⋅ 10a2

19

Page 20: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

191) 42x ⋅ 12x2 192) 18r3 ⋅ 12r3

193) 40x2 ⋅ 35x2 194) 5x ⋅ 10x

195) 2n3 ⋅ 24n2

196) 18k2 ⋅ 8k2

197) 24v ⋅ 30v3198) 27 p2

⋅ 14p

199) 9x ⋅ 10x2 200) 12n2 ⋅ 18n3

201) 3a ⋅ 3 3a3 202) 4 7k3 ⋅ 3k

20

Page 21: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

203) 2x2 ⋅ 6x 204) 5 28 p3

⋅ 4 14p3

205) 14x2 ⋅ 30x2 206) 12n ⋅ 6 9n3

207) 12r2 ⋅ 6r 208) 30x ⋅ 5 6x2

209) 3 14m3 ⋅ 42m 210) 3 6b3

⋅ 15b

211) 3v ⋅ 6 6v3 212) 4 18x ⋅ 15x2

213) 4 10n3 ⋅ 35n2 214) 4 20n3

⋅ 24n

215) 21k ⋅ 7 15k2 216) 15a2 ⋅ 28a2

217) 2 8x3 ⋅ 10x2 218) 4 6n ⋅ 2 6n3

219) 3 21x2 ⋅ 12x 220) 5 3 p2

⋅ 8p2

221) 3x ⋅ 2 12x2 222) 6 6k3 ⋅ 7 7k

223) 7 14n3 ⋅ 14n 224) 6 35m2

⋅ 5 14m3

225) 5 14r2 ⋅ 14r2 226) 30x ⋅ 6x3

227) 6n3 ⋅ 4 42n2 228) 3b3

⋅ 2 18b

21

Page 22: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

229) 35v3 ⋅ 5v3 230) 7 30x2

⋅ 12x3

231) 35x2 ⋅ 30x2 232) 6a3

⋅ 3a3

233) 5 30 p2 ⋅ 20p3 234) 7 12n3

⋅ 3 21n3

235) 12x ⋅ 8x2 236) 5 7k2 ⋅ 2 21k3

237) 2 30m3 ⋅ 6 10m2 238) 5 4n2

⋅ 2n2

239) 3 12r ⋅ 6r 240) 6x ⋅ 2 3x3

241) 3 28x3 ⋅ 7x2 242) 35b2

⋅ 7 14b3

243) 4 7n ⋅ 3 7n2 244) 5v ⋅ 7v3

245) 30a2 ⋅ 24a3 246) 35x ⋅ 6 35x3

247) 15x2 ⋅ 35x2 248) 35k2

⋅ 35k2

249) 2 18k ⋅ 18k3 250) 12x2 ⋅ 2 36x3

251) 2 28n ⋅ 28n3 252) 30 p3 ⋅ 18p

253) 3 15n3 ⋅ 7 30n 254) 7 6r3

⋅ 12r2

22

Page 23: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

255) 4 2n3 ⋅ 7 8n 256) 15m ⋅ 12m3

257) 6 8x2 ⋅ 6x 258) 7x3

⋅ 24x2

259) 4 3v2 ⋅ 21v 260) 5b ⋅ 3b

261) 7 15x2 ⋅ 10x3 262) 21a3

⋅ 7a

263) 5 30k2 ⋅ 30k 264) 18 p ⋅ 4 42p2

265) 2 21x2 ⋅ 14x3 266) 12n2

⋅ 7 42n2

267) 14r2 ⋅ 4 10r2 268) 30m3

⋅ 7 12m2

269) 7 3n2 ⋅ 15n2 270) 3x ⋅ 4 15x3

271) 28b2 ⋅ 42b 272) 3v3

⋅ 12v3

273) 8n2 ⋅ 4n3 274) 6a ⋅ 2 6a2

275) 12x2 ⋅ 5 12x 276) 6x2

⋅ 5x2

277) 2 7k2 ⋅ 5 2k 278) 21x3

⋅ 42x

279) 42m2 ⋅ 7m 280) 12 p ⋅ 6p3

23

Page 24: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

281) 2 8x ⋅ 14x 282) 30m ⋅ 6 42m

283) 25x2 ⋅ 4 25x 284) 5r3

⋅ 30r3

285) 5 12n2 ⋅ 42n 286) 10n2

⋅ 10n2

287) 7 3b3 ⋅ 21b 288) 8v3

⋅ 14v3

289) 12x2 ⋅ 7 20x2 290) 18x ⋅ 12x

291) 6a3 ⋅ 8a2 292) 5x ⋅ 5x

293) 14k2 ⋅ 6 4k 294) 7m ⋅ 7m3

295) 6 p ⋅ 3p3 296) 2n2 ⋅ 2n2

297) 14r3 ⋅ 3 7r2 298) 35x2

⋅ 7x

299) 7n2 ⋅ 6 7n3 300) 3 14b ⋅ 2 21b

301) 3 15v2 ⋅ 8 15v 302) 42a2

⋅ 18a3

303) 5 24x2 ⋅ 8 18x 304) 7n3

⋅ 56n2

305) 18k2 ⋅ 12k 306) 3 8m ⋅ 5 8m3

24

Page 25: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

307) 4 12n2 ⋅ 48n3 308) 6 21x2

⋅ 7 42x

309) 2 12x2 ⋅ 7x3 310) 42 p3

⋅ 8 14p3

311) 20x2 ⋅ 3 30x2 312) 2m3

⋅ 2m

313) 9 21n ⋅ 2 9n3 314) 2 56x ⋅ 42x3

315) 9 5r ⋅ 5 3r2 316) 12b2 ⋅ 2 15b2

317) 21n ⋅ 63n 318) 42v2 ⋅ 42v

319) 4 63x ⋅ 12x 320) 6a3 ⋅ 6a2

321) 4 42x ⋅ 7 18x 322) 63k2 ⋅ 9 56k

323) 54 p ⋅ 12p3 324) 7 15n2 ⋅ 45n2

325) 6 15m ⋅ 10m3 326) 6x3 ⋅ 3 30x2

327) 10r2 ⋅ 7 18r2 328) 63x ⋅ 21x

329) 20b2 ⋅ 20b2 330) 8 27x2

⋅ 4 3x2

331) 8 7n3 ⋅ 9 42n 332) 24v3

⋅ 6 21v3

25

Page 26: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

333) 5n2 ⋅ 7 48n3 334) 4 6a3

⋅ 5 21a3

335) 6k2 ⋅ 6 3k2 336) 6x ⋅ 8x3

337) 6x3 ⋅ 12x2 338) 9 5n2

⋅ 9n

339) 4 6m ⋅ 3m3 340) 8x2 ⋅ 8x2

341) 3 6 p3 ⋅ 5p2 342) 21n2

⋅ 5 15n

343) 10b2 ⋅ 2 35b 344) 40r ⋅ 5r3

345) 5 6x3 ⋅ 9 27x 346) 24n2

⋅ 18n

347) 30v ⋅ 3 5v 348) 35x ⋅ 7 28x3

349) 4 40x2 ⋅ 45x2 350) 4 24b3

⋅ 48b2

351) 56k2 ⋅ 4 28k3 352) 7 48a2

⋅ 6a

353) 5 6 p ⋅ 42p2 354) 10m ⋅ 2 30m3

355) 9 24r3 ⋅ 2 54r3 356) 10n2

⋅ 15n3

357) 3 25x2 ⋅ 15x2 358) 63n ⋅ 63n3

26

Page 27: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

359) 21v2 ⋅ 28v 360) 4 18b2

⋅ 7 54b

361) 24x ⋅ 18x3 362) 24n ⋅ 6 3n2

363) 3a3 ⋅ 6a3 364) 2 6k2

⋅ 2 15k2

365) 15x3 ⋅ 45x2 366) 14m3

⋅ 10m3

367) 8n2 ⋅ 10n 368) 8 6x ⋅ 14x

369) 6 12 p3 ⋅ 8 2p2 370) 3x3

⋅ 5x

371) 3r ⋅ 9 3r 372) 2b3 ⋅ 7 8b2

373) 6 9n ⋅ 7n3 374) 8b ⋅ 8 2b3

375) 5 45n ⋅ 8n3 376) 8 6v ⋅ 7v3

377) 4 42x ⋅ 7x 378) 5 30x3 ⋅ 54x3

379) 28a2 ⋅ 18a 380) 56k ⋅ 56k2

381) 42x3 ⋅ 21x2 382) 48x2

⋅ 24x3

383) 63 p3 ⋅ 4 14p 384) 9 12n2

⋅ 48n3

27

Page 28: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

385) 4 15m ⋅ 10m2 386) 18r3 ⋅ 30r

387) 40x3 ⋅ 2 35x2 388) 21n ⋅ 27n

389) 9 21v ⋅ 18v3 390) 40x ⋅ 7 5x

391) 45n2 ⋅ 7 45n 392) 30b3

⋅ 20b

393) 42a ⋅ 6a 394) 6k2 ⋅ 3k2

395) 7x3 ⋅ 56x 396) 8 15n2

⋅ 27n2

397) 5 6x3 ⋅ 12x 398) 12 p3

⋅ 10p2

399) 10m ⋅ 3 6m2 400) 14x2 ⋅ 4 18x

401) 8b3 ⋅ 2 2b 402) 4 3n ⋅ 4 6n

403) 21r2 ⋅ 7 3r3 404) 2 8x ⋅ 4 2x2

405) 3 14n ⋅ 2 2n 406) 4 3a3 ⋅ 7 7a3

407) 5 6v2 ⋅ 4 7v2 408) 6 21x ⋅ 6 42x3

409) 7 6x3 ⋅ 6 6x2 410) 7 14a2

⋅ 3 35a

28

Page 29: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

411) 5 12 p3 ⋅ 6 30p2 412) 3 5n ⋅ 6 20n2

413) 3 30x3 ⋅ 7 20x2 414) 6 36k ⋅ 6 30k3

415) 2 30m3 ⋅ 3 15m3 416) 5 12x2

⋅ 3 42x3

417) 6 4n ⋅ 5 8n2 418) 4 35r3 ⋅ 3 15r

419) 4 6b2 ⋅ 6 2b3 420) 3 21v2

⋅ 6 6v

421) 5 18x2 ⋅ 10x 422) 5 12n3

⋅ 3 2n2

423) 7 6k ⋅ 6 7k2 424) 7 5x3 ⋅ 7 6x3

425) 6 4a2 ⋅ 7 2a 426) 7 2x3

⋅ 3 6x

427) 5 35m ⋅ 3 35m 428) 6 2n2 ⋅ 5 6n2

429) 4 7 p3 ⋅ 7 35p3 430) 3 24x2

⋅ 5 30x

431) 2 6n ⋅ 5 30n3 432) 3 24b3 ⋅ 6 24b

433) 6 35r2 ⋅ 7 15r3 434) 3 15a ⋅ 4 18a2

435) 18n3 ⋅ 7 6n2 436) 20x ⋅ 5 15x3

29

Page 30: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

437) 4 21v2 ⋅ 5 6v2 438) 6 18x3

⋅ 3 3x3

439) 6 6x3 ⋅ 4 21x2 440) 7 6n2

⋅ 2 3n2

441) 5 5x2 ⋅ 2 6x 442) 7 10k ⋅ 2 14k3

443) 4 2n ⋅ 6n3 444) 6 2 p3 ⋅ 5 14p2

445) 3 42m ⋅ 7 21m 446) 3 7r2 ⋅ 2 42r3

447) 2 28x2 ⋅ 7 35x2 448) 42v2

⋅ 7 18v2

449) 2 18x ⋅ 3 18x 450) 7 18b3 ⋅ 5 30b2

451) 2 42n ⋅ 5 30n3 452) 3 30n3 ⋅ 6 15n2

453) 3 3k3 ⋅ 7 2k2 454) 6 6 p3

⋅ 6 6p2

455) 4 15a2 ⋅ 6 15a 456) 2 10x ⋅ 6 5x

457) 7 3n ⋅ 4 6n2 458) 6 15m ⋅ 2 21m

459) 5 2 p3 ⋅ 14p3 460) 4 8x2

⋅ 4 14x2

461) 3 14n ⋅ 4 12n 462) 5 7r2 ⋅ 3 6r3

30

Page 31: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

463) 2 3x3 ⋅ 5 6x3 464) 2 8b3

⋅ 2 12b3

465) 2 10n2 ⋅ 7 35n 466) 2 18a ⋅ 3 24a

467) 3 42v3 ⋅ 7 28v3 468) 3 12x2

⋅ 6 24x

469) 4 36x2 ⋅ 3 18x3 470) 5 5n ⋅ 7 15n2

471) 7 20x ⋅ 7 10x2 472) 3 18 p ⋅ 4 6p

473) 6 25k3 ⋅ 5 15k 474) 2 14n2

⋅ 5 21n3

475) 4 21r ⋅ 7 21r 476) 2 14n2 ⋅ 5 14n2

477) 3 6x3 ⋅ 2 14x3 478) 7 3m ⋅ 6 21m3

479) 6 6b2 ⋅ 2 14b2 480) 7 12v ⋅ 2 12v2

481) 3x3 ⋅ 3 6x 482) 2 6n2

⋅ 3 6n3

483) 3 14a ⋅ 5 35a2 484) 5 14 p2 ⋅ 28p2

485) 4 42k3 ⋅ 2 28k 486) 6 35x ⋅ 5 28x

487) 3 6m3 ⋅ 3 5m2 488) 7 35 p ⋅ 4 15p

31

Page 32: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

489) 3 3x2 ⋅ 5 3x2 490) 7 6n3

⋅ 2 18n3

491) 5 5n3 ⋅ 7 5n 492) 2 5b3

⋅ 6 2b3

493) 7 20r3 ⋅ 5 3r 494) 6x2

⋅ 7 6x3

495) 7 18n2 ⋅ 2 21n2 496) 7 6a ⋅ 2 21a2

497) 18v3 ⋅ 21v3 498) 3 5x ⋅ 2 6x

499) 4 2n ⋅ 5n3 500) 2 6x2 ⋅ 4 12x2

501) 6 5n2 ⋅ 7 2n3 502) 7 21b2

⋅ 8 3b2

503) 8 15x3 ⋅ 4 6x2 504) 5 35v ⋅ 7 10v

505) 3 20n2 ⋅ 8 40n2 506) 6 40a ⋅ 10 30a2

507) 4 20k ⋅ 4 50k2 508) 10 42n ⋅ 5 42n

509) 8 30x2 ⋅ 3 10x3 510) 7 70x2

⋅ 3 10x

511) 7 40m2 ⋅ 9 32m 512) 9 7 p ⋅ 5 8p3

513) 8 7x ⋅ 4 3x3 514) 3 56n ⋅ 9 28n3

32

Page 33: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

515) 5 12m2 ⋅ 7 6m 516) 8 63r2

⋅ 2 56r2

517) 3 3x ⋅ 9 6x2 518) 10 3n ⋅ 6 8n3

519) 3 20v2 ⋅ 4 10v3 520) 6 20b3

⋅ 10 40b2

521) 8 21x ⋅ 4 35x 522) 2 42a2 ⋅ 4 60a

523) 5 100x3 ⋅ 3 70x 524) 30 p3

⋅ 7 10p2

525) 10 90x3 ⋅ 2 90x2 526) 7 3k ⋅ 7 4k

527) 5 30n2 ⋅ 3 14n 528) 2 30m2

⋅ 40m2

529) 7 30r2 ⋅ 10 45r3 530) 9 30x ⋅ 3 60x2

531) 10 42n3 ⋅ 2 18n 532) 8 10b2

⋅ 9 35b

533) 6 42v ⋅ 6 48v 534) 4 6n3 ⋅ 2 24n

535) 7 10x ⋅ 8 27x2 536) 5 24a2 ⋅ 10 12a

537) 6 30x3 ⋅ 4 6x2 538) 2 63k ⋅ 2 35k3

539) 6 56x2 ⋅ 10 56x3 540) 8 15n ⋅ 10 15n2

33

Page 34: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

541) 8 25n3 ⋅ 36n 542) 6 2m3

⋅ 8m

543) 7 p2 ⋅ 3 70p3 544) 5 70x ⋅ 7 30x3

545) 3 90b2 ⋅ 7 10b2 546) 3 5x2

⋅ 9 5x2

547) 6 48r2 ⋅ 3 12r2 548) 10 8n ⋅ 2 10n3

549) 10 30v ⋅ 4 12v2 550) 6 8a2 ⋅ 7 2a2

551) 7 3b2 ⋅ 10 15b2 552) 5 21x2

⋅ 5 14x3

553) 7 3x3 ⋅ 8 4x 554) 2 14k2

⋅ 10 28k3

555) 3 2 p2 ⋅ 7 20p2 556) 8 27x ⋅ 4 70x

557) 5 8n3 ⋅ 9 2n3 558) 4 28m3

⋅ 5 21m3

559) 2 8n ⋅ 8 8n2 560) 2 24r2 ⋅ 10 8r

561) 18x2 ⋅ 3 6x2 562) 8 12v ⋅ 9 18v2

563) 8 10b3 ⋅ 80b 564) 4 20x2

⋅ 7 40x2

565) 4 54n ⋅ 10 5n 566) 5 24k ⋅ 4 30k

34

Page 35: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

567) 5 30x2 ⋅ 5 48x 568) 7 60a3

⋅ 5 45a3

569) 3 90x3 ⋅ 8 20x2 570) 4 50n3

⋅ 10 5n2

571) 3 35x3 ⋅ 3 12x2 572) 9 28m3

⋅ 3 14m

573) 2 8 p ⋅ 6 10p3 574) 2 28b2 ⋅ 7 63b2

575) 6 10n3 ⋅ 9 2n 576) 10r3

⋅ 6 10r2

577) 9 14n3 ⋅ 8 12n3 578) 2 20x3

⋅ 3 12x2

579) 3 24v3 ⋅ 6 40v3 580) 7 24b3

⋅ 4 27b

581) 6 60x2 ⋅ 5 60x 582) 10 15x2

⋅ 4 40x3

583) 5 21a2 ⋅ 6 27a3 584) 7 20k3

⋅ 4 15k

585) 6 12 p3 ⋅ 5 30p3 586) 3 15x ⋅ 8 35x2

587) 9 60m3 ⋅ 3 12m2 588) 8n3

⋅ 6 3n

589) 6 18x ⋅ 9 24x3 590) 7 14r3 ⋅ 7 54r

591) 10 24b2 ⋅ 4 54b 592) 8 20n3

⋅ 9 20n2

35

Page 36: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

593) 9 18v ⋅ 4 12v2 594) 7 42x3 ⋅ 5 21x

595) 8 42a2 ⋅ 9 15a3 596) 5 54n3

⋅ 6 30n3

597) 3k3 ⋅ 8 9k 598) 8 10x3

⋅ 5 14x3

599) 3 30x2 ⋅ 2 18x 600) 5 70n ⋅ 6 50n3

601) 187m3 ⋅ 17 323m2 602) 8 102 p ⋅ 10 27p2

603) 18 95x ⋅ 20 38x2 604) 15 33n3 ⋅ 14 88n2

605) 3 119b3 ⋅ 4 57b3 606) 7 15x3

⋅ 4 60x

607) 4 18n2 ⋅ 20 11n3 608) 2 247r2

⋅ 3 133r

609) 14 42a3 ⋅ 18 112a3 610) 18 30v2

⋅ 9 60v2

611) 10 187x3 ⋅ 11 221x3 612) 9 16x2

⋅ 15 36x

613) 17 252a2 ⋅ 70a3 614) 15 18k3

⋅ 22k2

615) 19 126 p2 ⋅ 14 21p2 616) 20 20x ⋅ 18 10x2

617) 17 95n3 ⋅ 2 57n 618) 14 57m2

⋅ 5 30m3

36

Page 37: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

619) 12 323r ⋅ 11 30r 620) 8 15x ⋅ 13 60x

621) 2 150b2 ⋅ 11 255b 622) 5 285n3

⋅ 4 190n2

623) 6 52v3 ⋅ 13 195v 624) 19 77x3

⋅ 12 143x3

625) 15 26n ⋅ 2 78n 626) 16 6k2 ⋅ 3 10k3

627) 15 304a3 ⋅ 12 228a3 628) 3 12x3

⋅ 15 340x3

629) 19 8x ⋅ 6 16x2 630) 19 34n3 ⋅ 14 51n

631) 16 221m3 ⋅ 11 130m3 632) 9 234x ⋅ 12 39x3

633) 4 34n2 ⋅ 20 52n2 634) 12 51 p2

⋅ 4 272p

635) 3 266b2 ⋅ 5 112b 636) 3 112x3

⋅ 18 28x3

637) 2 126r ⋅ 5 28r3 638) 18 135n ⋅ 5 210n3

639) 12 76v3 ⋅ 8 38v3 640) 15 285x2

⋅ 15 135x2

641) 9 126a ⋅ 8 210a 642) 18 55x2 ⋅ 10 88x

643) 20 300a ⋅ 2 210a2 644) 14 15 p2 ⋅ 20 120p3

37

Page 38: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

645) 15 65x3 ⋅ 8 126x2 646) 17 154k3

⋅ 14 11k

647) 7 285n ⋅ 12 19n2 648) 12 51m ⋅ 15 120m

649) 20 285r2 ⋅ 2 57r 650) 19 45x3

⋅ 15 104x2

651) 7 91b2 ⋅ 17 91b 652) 9 16n2

⋅ 6 88n

653) 8 6v3 ⋅ 4 114v 654) 14 104x3

⋅ 260x

655) 6 5n3 ⋅ 11 8n 656) 20 221a ⋅ 19 182a2

657) 7 6k ⋅ 2 84k3 658) 15 252x2 ⋅ 5 98x3

659) 12 130x ⋅ 12 60x 660) 9 98n3 ⋅ 13 182n3

661) 6 140m2 ⋅ 5 190m2 662) 3 126 p ⋅ 2 84p

663) 3 70n3 ⋅ 16 140n2 664) 6 44b2

⋅ 11 66b3

665) 5 30x ⋅ 2 130x 666) 15 140n2 ⋅ 10 133n3

667) 12 66x3 ⋅ 17 132x 668) 18 165a ⋅ 6 55a2

669) 9 133r ⋅ 8 91r2 670) 14 8v ⋅ 6 19v2

38

Page 39: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

671) 11 209x ⋅ 18 57x 672) 17 50x2 ⋅ 5 40x

673) 3 34n3 ⋅ 40n 674) 14 171k3

⋅ 20 171k2

675) 8 68x ⋅ 9 255x 676) 4 30 p2 ⋅ 14 90p

677) 13 130r2 ⋅ 14 195r3 678) 2 35n3

⋅ 9 55n

679) 14 140m3 ⋅ 5 360m3 680) 10 66x3

⋅ 30x

681) 14 108n2 ⋅ 15 108n2 682) 17 120b ⋅ 19 50b

683) 20 114v3 ⋅ 2 72v3 684) 16 102x2

⋅ 20 102x

685) 15 48n2 ⋅ 20 102n 686) 12 28a ⋅ 13 8a3

687) 9 63k3 ⋅ 6 70k 688) 3 70x ⋅ 18 28x2

689) 6 12 p2 ⋅ 11 51p3 690) 18 15n3

⋅ 14 33n

691) 3 133m2 ⋅ 10 119m3 692) 13 45n2

⋅ 17 300n

693) 21x2 ⋅ 3 30x3 694) 12 150b2

⋅ 3 130b

695) 6 18 p ⋅ 17 48p 696) 4 85r3 ⋅ 10 5r3

39

Page 40: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

697) 16 198x ⋅ 18 400x3 698) 4 224n ⋅ 13 182n3

699) 13 12a ⋅ 12 3a2 700) 10 30v3 ⋅ 19 10v

40

Page 41: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

MATHEMANIA.COM

Multiplication of radicals - 2 monomials with variables

Multiply radicals:

1) 5x ⋅ 6x2

x 30x

2) 20k ⋅ 20k3

20k2

3) 20n2 ⋅ 20n2

20n2

4) 10a3 ⋅ 20a

10a22

5) 3 p ⋅ 5p3

p215

6) 3r ⋅ 3r2

3r r

7) 10m3 ⋅ 15m2

5m26m

8) 3x2 ⋅ 3x3

3x2 x

9) 2x2 ⋅ 5x2

x210

10) 10n ⋅ 6n2

2n 15n

1

Page 42: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

11) 12v2 ⋅ 6v2

6v22

12) 8b3 ⋅ 10b

4b25

13) 15n3 ⋅ 15n3

15n3

14) 10x ⋅ 6x

2x 15

15) 6a2 ⋅ 6a2

6a2

16) 6n2 ⋅ 3n2

3n22

17) 6x3 ⋅ 3x

3x22

18) 8x2 ⋅ 10x3

4x25x

19) 5 p3 ⋅ 20p2

10 p2 p

20) 3m3 ⋅ 5m

m215

2

Page 43: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

21) 2n ⋅ 3n2

n 6n

22) 6x ⋅ 10x

2x 15

23) 3b3 ⋅ 2b

b26

24) 2n ⋅ 2n3

2n2

25) 6x3 ⋅ 2x

2x23

26) 3x ⋅ 2x2

x 6x

27) 8k ⋅ 8k3

8k2

28) 8a2 ⋅ 8a2

8a2

29) 8x2 ⋅ 3x3

2x26x

30) 15x2 ⋅ 6x3

3x210x

3

Page 44: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

31) 12m3 ⋅ 3m

6m2

32) 6 p ⋅ 2p

2p 3

33) 2n3 ⋅ 2n3

2n3

34) 8r3 ⋅ 6r3

4r33

35) 12x3 ⋅ 5x2

2x215x

36) 5n2 ⋅ 15n

5n 3n

37) 2x ⋅ 5x3

x210

38) 10b ⋅ 2b3

2b25

39) 5v2 ⋅ 10v3

5v22v

40) 2a2 ⋅ 2a2

2a2

4

Page 45: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

41) 2k3 ⋅ 3k2

k26k

42) 3x2 ⋅ 2x

x 6x

43) 10x2 ⋅ 2x

2x 5x

44) 2n3 ⋅ 10n2

2n25n

45) 2m ⋅ 2m

2m

46) 6 p3 ⋅ 8p3

4p33

47) 2n3 ⋅ 8n

4n2

48) 6x2 ⋅ 2x

2x 3x

49) 3r3 ⋅ 16r3

4r33

50) 12b ⋅ 3b2

6b b

5

Page 46: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

51) 20a2 ⋅ 15a2

10a23

52) 3x ⋅ 6x3

3x22

53) 15v2 ⋅ 12v2

6v25

54) 25x ⋅ 10x3

5x210

55) 25a2 ⋅ 5a

5a 5a

56) 10x2 ⋅ 10x

10x x

57) 6 p3 ⋅ 2p2

2 p23p

58) 5n ⋅ 10n3

5n22

59) 2m3 ⋅ 2m

2m2

60) 3r2 ⋅ 2r3

r26r

6

Page 47: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

61) 2n ⋅ 6n

2n 3

62) 3b ⋅ 2b3

b26

63) 8x2 ⋅ 5x2

2x210

64) 2v2 ⋅ 8v

4v v

65) 3n3 ⋅ 3n2

3n2 n

66) 20x2 ⋅ 20x

20x x

67) 20k ⋅ 15k

10k 3

68) 6x ⋅ 6x

6x

69) 10x2 ⋅ 12x3

2x230x

70) 8n3 ⋅ 8n

8n2

7

Page 48: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

71) 12m2 ⋅ 12m

12m m

72) 10n3 ⋅ 10n3

10n3

73) 15 p3 ⋅ 10p

5 p26

74) 4b2 ⋅ 4b2

4b2

75) 3x2 ⋅ 4x2

2x23

76) 5r2 ⋅ 12r

2r 15r

77) 8a2 ⋅ 2a2

4a2

78) 15n3 ⋅ 12n

6n25

79) 3v ⋅ 9v

3v 3

80) 15x2 ⋅ 3x3

3x25x

8

Page 49: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

81) 2k3 ⋅ 3k

k26

82) 10a ⋅ 2a2

2a 5a

83) 12 p3 ⋅ 2p

2 p26

84) 6n3 ⋅ 6n

6n2

85) 15x ⋅ 6x3

3x210

86) 10r ⋅ 5r2

5r 2r

87) 2n ⋅ 8n

4n

88) 15b ⋅ 10b3

5b26

89) 2m2 ⋅ 6m

2m 3m

90) 3n2 ⋅ 3n2

3n2

9

Page 50: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

91) 8v2 ⋅ 12v3

4v26v

92) 15x3 ⋅ 5x3

5x33

93) 20a ⋅ 10a2

10a 2a

94) 8k3 ⋅ 2k2

4k2 k

95) 4x ⋅ 20x

4x 5

96) 12n3 ⋅ 5n3

2n315

97) 10 p3 ⋅ 2p3

2 p35

98) 12m2 ⋅ 15m2

6m25

99) 15x3 ⋅ 12x2

6x25x

100) 20b3 ⋅ 12b2

4b215b

10

Page 51: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

101) 12r3 ⋅ 12r2

12r2 r

102) 8x ⋅ 3x3

2x26

103) 20n ⋅ 30n

10n 6

104) 5x2 ⋅ 42x

x 210x

105) 21a ⋅ 18a3

3a242

106) 18x ⋅ 10x2

6x 5x

107) 24n2 ⋅ 5n2

2n230

108) 21v3 ⋅ 27v2

9v27v

109) 4k ⋅ 8k

4k 2

110) 8 p3 ⋅ 6p3

4p33

11

Page 52: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

111) 12n ⋅ 12n2

12n n

112) 30m3 ⋅ 42m2

6m235m

113) 6r ⋅ 7r2

r 42r

114) 35x3 ⋅ 5x

5x27

115) 2x2 ⋅ 8x3

4x2 x

116) 24n2 ⋅ 3n3

6n22n

117) 54v2 ⋅ 54v3

54v2 v

118) 63b ⋅ 35b3

21b25

119) 12x ⋅ 21x

6x 7

120) 12a ⋅ 24a3

12a22

12

Page 53: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

121) 28k3 ⋅ 21k3

14k33

122) 6n3 ⋅ 7n

n242

123) 42 p3 ⋅ 12p3

6 p314

124) 30m3 ⋅ 48m2

12m210m

125) 12n ⋅ 56n3

4n242

126) 54x2 ⋅ 54x

54x x

127) 54 p ⋅ 48p

36 p 2

128) 12n2 ⋅ 6n2

6n22

129) 6x3 ⋅ 18x3

6x33

130) 40b2 ⋅ 27b3

6b230b

13

Page 54: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

131) 10r ⋅ 24r2

4r 15r

132) 21x2 ⋅ 54x3

9x214x

133) 15n3 ⋅ 6n

3n210

134) 6a ⋅ 3a

3a 2

135) 24v3 ⋅ 12v3

12v32

136) 27x ⋅ 3x3

9x2

137) 24x2 ⋅ 21x

6x 14x

138) 12n ⋅ 7n3

2n221

139) 21k3 ⋅ 10k2

k2210k

140) 18 p2 ⋅ 8p

12p p

14

Page 55: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

141) 5n3 ⋅ 6n

n230

142) 6r ⋅ 3r2

3r 2r

143) 10m2 ⋅ 18m

6m 5m

144) 6x ⋅ 6x2

6x x

145) 45n2 ⋅ 20n2

30n2

146) 5v ⋅ 25v2

5v 5v

147) 18x ⋅ 10x3

6x25

148) 63b3 ⋅ 35b2

21b25b

149) 6x3 ⋅ 42x

6x27

150) 12n ⋅ 42n

6n 14

15

Page 56: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

151) 14k2 ⋅ 8k

4k 7k

152) 35x3 ⋅ 12x2

2x2105x

153) 30a3 ⋅ 12a3

6a310

154) 14 p ⋅ 10p3

2p235

155) 49n2 ⋅ 63n

21n 7n

156) 30m ⋅ 30m3

30m2

157) 5n2 ⋅ 45n2

15n2

158) 48r ⋅ 24r2

24r 2r

159) 10b ⋅ 15b

5b 6

160) 10x ⋅ 18x2

6x 5x

16

Page 57: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

161) 42r3 ⋅ 27r3

9r314

162) 15n ⋅ 30n3

15n22

163) 45x2 ⋅ 28x2

6x235

164) 30a3 ⋅ 20a2

10a26a

165) 6x ⋅ 24x

12x

166) 35x3 ⋅ 15x3

5x321

167) 27n3 ⋅ 24n2

18n22n

168) 18k ⋅ 24k3

12k23

169) 10 p3 ⋅ 15p

5 p26

170) 28x ⋅ 63x

42x

17

Page 58: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

171) 10m2 ⋅ 8m

4m 5m

172) 12r ⋅ 14r2

2r 42r

173) 7x2 ⋅ 7x

7x x

174) 40n3 ⋅ 30n

20n23

175) 28b3 ⋅ 12b

4b221

176) 8v2 ⋅ 72v3

24v2 v

177) 12x ⋅ 3x

6x

178) 6n3 ⋅ 2n

2n23

179) 42k2 ⋅ 24k3

12k27k

180) 21a2 ⋅ 6a3

3a214a

18

Page 59: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

181) 24x2 ⋅ 6x2

12x2

182) 20 p ⋅ 30p2

10p 6p

183) 42n ⋅ 15n

3n 70

184) 42m3 ⋅ 72m2

12m221m

185) 12n2 ⋅ 30n3

6n210n

186) 12b ⋅ 48b2

24b b

187) 56r ⋅ 63r3

42r22

188) 54x3 ⋅ 12x2

18x22x

189) 35n2 ⋅ 35n3

35n2 n

190) 25a ⋅ 10a2

5a 10a

19

Page 60: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

191) 42x ⋅ 12x2

6x 14x

192) 18r3 ⋅ 12r3

6r36

193) 40x2 ⋅ 35x2

10x214

194) 5x ⋅ 10x

5x 2

195) 2n3 ⋅ 24n2

4n23n

196) 18k2 ⋅ 8k2

12k2

197) 24v ⋅ 30v3

12v25

198) 27 p2 ⋅ 14p

3p 42p

199) 9x ⋅ 10x2

3x 10x

200) 12n2 ⋅ 18n3

6n26n

201) 3a ⋅ 3 3a3

9a2

202) 4 7k3 ⋅ 3k

4k221

20

Page 61: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

203) 2x2 ⋅ 6x

2x 3x

204) 5 28 p3 ⋅ 4 14p3

280p32

205) 14x2 ⋅ 30x2

2x2105

206) 12n ⋅ 6 9n3

36n23

207) 12r2 ⋅ 6r

6r 2r

208) 30x ⋅ 5 6x2

30x 5x

209) 3 14m3 ⋅ 42m

42m23

210) 3 6b3 ⋅ 15b

9b210

211) 3v ⋅ 6 6v3

18v22

212) 4 18x ⋅ 15x2

12x 30x

213) 4 10n3 ⋅ 35n2

20n214n

214) 4 20n3 ⋅ 24n

16n230

215) 21k ⋅ 7 15k2

21k 35k

216) 15a2 ⋅ 28a2

2a2105

217) 2 8x3 ⋅ 10x2

8x25x

218) 4 6n ⋅ 2 6n3

48n2

219) 3 21x2 ⋅ 12x

18x 7x

220) 5 3 p2 ⋅ 8p2

10p26

221) 3x ⋅ 2 12x2

12x x

222) 6 6k3 ⋅ 7 7k

42k242

223) 7 14n3 ⋅ 14n

98n2

224) 6 35m2 ⋅ 5 14m3

210m210m

225) 5 14r2 ⋅ 14r2

70r2

226) 30x ⋅ 6x3

6x25

227) 6n3 ⋅ 4 42n2

24n27n

228) 3b3 ⋅ 2 18b

6b26

21

Page 62: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

229) 35v3 ⋅ 5v3

5v37

230) 7 30x2 ⋅ 12x3

42x210x

231) 35x2 ⋅ 30x2

5x242

232) 6a3 ⋅ 3a3

3a32

233) 5 30 p2 ⋅ 20p3

50 p26p

234) 7 12n3 ⋅ 3 21n3

126n37

235) 12x ⋅ 8x2

4x 6x

236) 5 7k2 ⋅ 2 21k3

70k23k

237) 2 30m3 ⋅ 6 10m2

120m23m

238) 5 4n2 ⋅ 2n2

10n22

239) 3 12r ⋅ 6r

18r 2

240) 6x ⋅ 2 3x3

6x22

241) 3 28x3 ⋅ 7x2

42x2 x

242) 35b2 ⋅ 7 14b3

49b210b

243) 4 7n ⋅ 3 7n2

84n n

244) 5v ⋅ 7v3

v235

245) 30a2 ⋅ 24a3

12a25a

246) 35x ⋅ 6 35x3

210x2

247) 15x2 ⋅ 35x2

5x221

248) 35k2 ⋅ 35k2

35k2

249) 2 18k ⋅ 18k3

36k2

250) 12x2 ⋅ 2 36x3

24x23x

251) 2 28n ⋅ 28n3

56n2

252) 30 p3 ⋅ 18p

6p215

253) 3 15n3 ⋅ 7 30n

315n22

254) 7 6r3 ⋅ 12r2

42r22r

22

Page 63: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

255) 4 2n3 ⋅ 7 8n

112n2

256) 15m ⋅ 12m3

6m25

257) 6 8x2 ⋅ 6x

24x 3x

258) 7x3 ⋅ 24x2

2x242x

259) 4 3v2 ⋅ 21v

12v 7v

260) 5b ⋅ 3b

b 15

261) 7 15x2 ⋅ 10x3

35x26x

262) 21a3 ⋅ 7a

7a23

263) 5 30k2 ⋅ 30k

150k k

264) 18 p ⋅ 4 42p2

24p 21p

265) 2 21x2 ⋅ 14x3

14x26x

266) 12n2 ⋅ 7 42n2

42n214

267) 14r2 ⋅ 4 10r2

8r235

268) 30m3 ⋅ 7 12m2

42m210m

269) 7 3n2 ⋅ 15n2

21n25

270) 3x ⋅ 4 15x3

12x25

271) 28b2 ⋅ 42b

14b 6b

272) 3v3 ⋅ 12v3

6v3

273) 8n2 ⋅ 4n3

4n22n

274) 6a ⋅ 2 6a2

12a a

275) 12x2 ⋅ 5 12x

60x x

276) 6x2 ⋅ 5x2

x230

277) 2 7k2 ⋅ 5 2k

10k 14k

278) 21x3 ⋅ 42x

21x22

279) 42m2 ⋅ 7m

7m 6m

280) 12 p ⋅ 6p3

6p22

23

Page 64: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

281) 2 8x ⋅ 14x

8x 7

282) 30m ⋅ 6 42m

36m 35

283) 25x2 ⋅ 4 25x

100x x

284) 5r3 ⋅ 30r3

5r36

285) 5 12n2 ⋅ 42n

30n 14n

286) 10n2 ⋅ 10n2

10n2

287) 7 3b3 ⋅ 21b

21b27

288) 8v3 ⋅ 14v3

4v37

289) 12x2 ⋅ 7 20x2

28x215

290) 18x ⋅ 12x

6x 6

291) 6a3 ⋅ 8a2

4a23a

292) 5x ⋅ 5x

5x

293) 14k2 ⋅ 6 4k

12k 14k

294) 7m ⋅ 7m3

7m2

295) 6 p ⋅ 3p3

3 p22

296) 2n2 ⋅ 2n2

2n2

297) 14r3 ⋅ 3 7r2

21r22r

298) 35x2 ⋅ 7x

7x 5x

299) 7n2 ⋅ 6 7n3

42n2 n

300) 3 14b ⋅ 2 21b

42b 6

301) 3 15v2 ⋅ 8 15v

360v v

302) 42a2 ⋅ 18a3

6a221a

303) 5 24x2 ⋅ 8 18x

480x 3x

304) 7n3 ⋅ 56n2

14n22n

305) 18k2 ⋅ 12k

6k 6k

306) 3 8m ⋅ 5 8m3

120m2

24

Page 65: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

307) 4 12n2 ⋅ 48n3

96n2 n

308) 6 21x2 ⋅ 7 42x

882x 2x

309) 2 12x2 ⋅ 7x3

4x221x

310) 42 p3 ⋅ 8 14p3

112p33

311) 20x2 ⋅ 3 30x2

30x26

312) 2m3 ⋅ 2m

2m2

313) 9 21n ⋅ 2 9n3

54n221

314) 2 56x ⋅ 42x3

56x23

315) 9 5r ⋅ 5 3r2

45r 15r

316) 12b2 ⋅ 2 15b2

12b25

317) 21n ⋅ 63n

21n 3

318) 42v2 ⋅ 42v

42v v

319) 4 63x ⋅ 12x

24x 21

320) 6a3 ⋅ 6a2

6a2 a

321) 4 42x ⋅ 7 18x

168x 21

322) 63k2 ⋅ 9 56k

378k 2k

323) 54 p ⋅ 12p3

18 p22

324) 7 15n2 ⋅ 45n2

105n23

325) 6 15m ⋅ 10m3

30m26

326) 6x3 ⋅ 3 30x2

18x25x

327) 10r2 ⋅ 7 18r2

42r25

328) 63x ⋅ 21x

21x 3

329) 20b2 ⋅ 20b2

20b2

330) 8 27x2 ⋅ 4 3x2

288x2

331) 8 7n3 ⋅ 9 42n

504n26

332) 24v3 ⋅ 6 21v3

36v314

25

Page 66: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

333) 5n2 ⋅ 7 48n3

28n215n

334) 4 6a3 ⋅ 5 21a3

60a314

335) 6k2 ⋅ 6 3k2

18k22

336) 6x ⋅ 8x3

4x23

337) 6x3 ⋅ 12x2

6x22x

338) 9 5n2 ⋅ 9n

27n 5n

339) 4 6m ⋅ 3m3

12m22

340) 8x2 ⋅ 8x2

8x2

341) 3 6 p3 ⋅ 5p2

3 p230p

342) 21n2 ⋅ 5 15n

15n 35n

343) 10b2 ⋅ 2 35b

10b 14b

344) 40r ⋅ 5r3

10r22

345) 5 6x3 ⋅ 9 27x

405x22

346) 24n2 ⋅ 18n

12n 3n

347) 30v ⋅ 3 5v

15v 6

348) 35x ⋅ 7 28x3

98x25

349) 4 40x2 ⋅ 45x2

120x22

350) 4 24b3 ⋅ 48b2

96b22b

351) 56k2 ⋅ 4 28k3

112k22k

352) 7 48a2 ⋅ 6a

84a 2a

353) 5 6 p ⋅ 42p2

30 p 7p

354) 10m ⋅ 2 30m3

20m23

355) 9 24r3 ⋅ 2 54r3

648r3

356) 10n2 ⋅ 15n3

5n26n

357) 3 25x2 ⋅ 15x2

15x215

358) 63n ⋅ 63n3

63n2

26

Page 67: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

359) 21v2 ⋅ 28v

14v 3v

360) 4 18b2 ⋅ 7 54b

504b 3b

361) 24x ⋅ 18x3

12x23

362) 24n ⋅ 6 3n2

36n 2n

363) 3a3 ⋅ 6a3

3a32

364) 2 6k2 ⋅ 2 15k2

12k210

365) 15x3 ⋅ 45x2

15x23x

366) 14m3 ⋅ 10m3

2m335

367) 8n2 ⋅ 10n

4n 5n

368) 8 6x ⋅ 14x

16x 21

369) 6 12 p3 ⋅ 8 2p2

96 p26p

370) 3x3 ⋅ 5x

x215

371) 3r ⋅ 9 3r

27r

372) 2b3 ⋅ 7 8b2

28b2 b

373) 6 9n ⋅ 7n3

18n27

374) 8b ⋅ 8 2b3

32b2

375) 5 45n ⋅ 8n3

30n210

376) 8 6v ⋅ 7v3

8v242

377) 4 42x ⋅ 7x

28x 6

378) 5 30x3 ⋅ 54x3

90x35

379) 28a2 ⋅ 18a

6a 14a

380) 56k ⋅ 56k2

56k k

381) 42x3 ⋅ 21x2

21x22x

382) 48x2 ⋅ 24x3

24x22x

383) 63 p3 ⋅ 4 14p

84 p22

384) 9 12n2 ⋅ 48n3

216n2 n

27

Page 68: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

385) 4 15m ⋅ 10m2

20m 6m

386) 18r3 ⋅ 30r

6r215

387) 40x3 ⋅ 2 35x2

20x214x

388) 21n ⋅ 27n

9n 7

389) 9 21v ⋅ 18v3

27v242

390) 40x ⋅ 7 5x

70x 2

391) 45n2 ⋅ 7 45n

315n n

392) 30b3 ⋅ 20b

10b26

393) 42a ⋅ 6a

6a 7

394) 6k2 ⋅ 3k2

3k22

395) 7x3 ⋅ 56x

14x22

396) 8 15n2 ⋅ 27n2

72n25

397) 5 6x3 ⋅ 12x

30x22

398) 12 p3 ⋅ 10p2

2p230p

399) 10m ⋅ 3 6m2

6m 15m

400) 14x2 ⋅ 4 18x

24x 7x

401) 8b3 ⋅ 2 2b

8b2

402) 4 3n ⋅ 4 6n

48n 2

403) 21r2 ⋅ 7 3r3

21r27r

404) 2 8x ⋅ 4 2x2

32x x

405) 3 14n ⋅ 2 2n

12n 7

406) 4 3a3 ⋅ 7 7a3

28a321

407) 5 6v2 ⋅ 4 7v2

20v242

408) 6 21x ⋅ 6 42x3

756x22

409) 7 6x3 ⋅ 6 6x2

252x2 x

410) 7 14a2 ⋅ 3 35a

147a 10a

28

Page 69: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

411) 5 12 p3 ⋅ 6 30p2

180 p210p

412) 3 5n ⋅ 6 20n2

180n n

413) 3 30x3 ⋅ 7 20x2

210x26x

414) 6 36k ⋅ 6 30k3

216k230

415) 2 30m3 ⋅ 3 15m3

90m32

416) 5 12x2 ⋅ 3 42x3

90x214x

417) 6 4n ⋅ 5 8n2

120n 2n

418) 4 35r3 ⋅ 3 15r

60r221

419) 4 6b2 ⋅ 6 2b3

48b23b

420) 3 21v2 ⋅ 6 6v

54v 14v

421) 5 18x2 ⋅ 10x

30x 5x

422) 5 12n3 ⋅ 3 2n2

30n26n

423) 7 6k ⋅ 6 7k2

42k 42k

424) 7 5x3 ⋅ 7 6x3

49x330

425) 6 4a2 ⋅ 7 2a

84a 2a

426) 7 2x3 ⋅ 3 6x

42x23

427) 5 35m ⋅ 3 35m

525m

428) 6 2n2 ⋅ 5 6n2

60n23

429) 4 7 p3 ⋅ 7 35p3

196 p35

430) 3 24x2 ⋅ 5 30x

180x 5x

431) 2 6n ⋅ 5 30n3

60n25

432) 3 24b3 ⋅ 6 24b

432b2

433) 6 35r2 ⋅ 7 15r3

210r221r

434) 3 15a ⋅ 4 18a2

36a 30a

435) 18n3 ⋅ 7 6n2

42n23n

436) 20x ⋅ 5 15x3

50x23

29

Page 70: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

437) 4 21v2 ⋅ 5 6v2

60v214

438) 6 18x3 ⋅ 3 3x3

54x36

439) 6 6x3 ⋅ 4 21x2

72x214x

440) 7 6n2 ⋅ 2 3n2

42n22

441) 5 5x2 ⋅ 2 6x

10x 30x

442) 7 10k ⋅ 2 14k3

28k235

443) 4 2n ⋅ 6n3

8n23

444) 6 2 p3 ⋅ 5 14p2

60p27p

445) 3 42m ⋅ 7 21m

441m 2

446) 3 7r2 ⋅ 2 42r3

42r26r

447) 2 28x2 ⋅ 7 35x2

196x25

448) 42v2 ⋅ 7 18v2

42v221

449) 2 18x ⋅ 3 18x

108x

450) 7 18b3 ⋅ 5 30b2

210b215b

451) 2 42n ⋅ 5 30n3

60n235

452) 3 30n3 ⋅ 6 15n2

270n22n

453) 3 3k3 ⋅ 7 2k2

21k26k

454) 6 6 p3 ⋅ 6 6p2

216p2 p

455) 4 15a2 ⋅ 6 15a

360a a

456) 2 10x ⋅ 6 5x

60x 2

457) 7 3n ⋅ 4 6n2

84n 2n

458) 6 15m ⋅ 2 21m

36m 35

459) 5 2 p3 ⋅ 14p3

10 p37

460) 4 8x2 ⋅ 4 14x2

64x27

461) 3 14n ⋅ 4 12n

24n 42

462) 5 7r2 ⋅ 3 6r3

15r242r

30

Page 71: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

463) 2 3x3 ⋅ 5 6x3

30x32

464) 2 8b3 ⋅ 2 12b3

16b36

465) 2 10n2 ⋅ 7 35n

70n 14n

466) 2 18a ⋅ 3 24a

72a 3

467) 3 42v3 ⋅ 7 28v3

294v36

468) 3 12x2 ⋅ 6 24x

216x 2x

469) 4 36x2 ⋅ 3 18x3

216x22x

470) 5 5n ⋅ 7 15n2

175n 3n

471) 7 20x ⋅ 7 10x2

490x 2x

472) 3 18 p ⋅ 4 6p

72p 3

473) 6 25k3 ⋅ 5 15k

150k215

474) 2 14n2 ⋅ 5 21n3

70n26n

475) 4 21r ⋅ 7 21r

588r

476) 2 14n2 ⋅ 5 14n2

140n2

477) 3 6x3 ⋅ 2 14x3

12x321

478) 7 3m ⋅ 6 21m3

126m27

479) 6 6b2 ⋅ 2 14b2

24b221

480) 7 12v ⋅ 2 12v2

168v v

481) 3x3 ⋅ 3 6x

9x22

482) 2 6n2 ⋅ 3 6n3

36n2 n

483) 3 14a ⋅ 5 35a2

105a 10a

484) 5 14 p2 ⋅ 28p2

70p22

485) 4 42k3 ⋅ 2 28k

112k26

486) 6 35x ⋅ 5 28x

420x 5

487) 3 6m3 ⋅ 3 5m2

9m230m

488) 7 35 p ⋅ 4 15p

140p 21

31

Page 72: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

489) 3 3x2 ⋅ 5 3x2

45x2

490) 7 6n3 ⋅ 2 18n3

84n33

491) 5 5n3 ⋅ 7 5n

175n2

492) 2 5b3 ⋅ 6 2b3

12b310

493) 7 20r3 ⋅ 5 3r

70r215

494) 6x2 ⋅ 7 6x3

42x2 x

495) 7 18n2 ⋅ 2 21n2

42n242

496) 7 6a ⋅ 2 21a2

42a 14a

497) 18v3 ⋅ 21v3

3v342

498) 3 5x ⋅ 2 6x

6x 30

499) 4 2n ⋅ 5n3

4n210

500) 2 6x2 ⋅ 4 12x2

48x22

501) 6 5n2 ⋅ 7 2n3

42n210n

502) 7 21b2 ⋅ 8 3b2

168b27

503) 8 15x3 ⋅ 4 6x2

96x210x

504) 5 35v ⋅ 7 10v

175v 14

505) 3 20n2 ⋅ 8 40n2

480n22

506) 6 40a ⋅ 10 30a2

1200a 3a

507) 4 20k ⋅ 4 50k2

160k 10k

508) 10 42n ⋅ 5 42n

2100n

509) 8 30x2 ⋅ 3 10x3

240x23x

510) 7 70x2 ⋅ 3 10x

210x 7x

511) 7 40m2 ⋅ 9 32m

1008m 5m

512) 9 7 p ⋅ 5 8p3

90p214

513) 8 7x ⋅ 4 3x3

32x221

514) 3 56n ⋅ 9 28n3

756n22

32

Page 73: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

515) 5 12m2 ⋅ 7 6m

210m 2m

516) 8 63r2 ⋅ 2 56r2

672r22

517) 3 3x ⋅ 9 6x2

81x 2x

518) 10 3n ⋅ 6 8n3

120n26

519) 3 20v2 ⋅ 4 10v3

120v22v

520) 6 20b3 ⋅ 10 40b2

1200b22b

521) 8 21x ⋅ 4 35x

224x 15

522) 2 42a2 ⋅ 4 60a

48a 70a

523) 5 100x3 ⋅ 3 70x

150x270

524) 30 p3 ⋅ 7 10p2

70p23p

525) 10 90x3 ⋅ 2 90x2

1800x2 x

526) 7 3k ⋅ 7 4k

98k 3

527) 5 30n2 ⋅ 3 14n

30n 105n

528) 2 30m2 ⋅ 40m2

40m23

529) 7 30r2 ⋅ 10 45r3

1050r26r

530) 9 30x ⋅ 3 60x2

810x 2x

531) 10 42n3 ⋅ 2 18n

120n221

532) 8 10b2 ⋅ 9 35b

360b 14b

533) 6 42v ⋅ 6 48v

432v 14

534) 4 6n3 ⋅ 2 24n

96n2

535) 7 10x ⋅ 8 27x2

168x 30x

536) 5 24a2 ⋅ 10 12a

600a 2a

537) 6 30x3 ⋅ 4 6x2

144x25x

538) 2 63k ⋅ 2 35k3

84k25

539) 6 56x2 ⋅ 10 56x3

3360x2 x

540) 8 15n ⋅ 10 15n2

1200n n

33

Page 74: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

541) 8 25n3 ⋅ 36n

240n2

542) 6 2m3 ⋅ 8m

24m2

543) 7 p2 ⋅ 3 70p3

21 p210p

544) 5 70x ⋅ 7 30x3

350x221

545) 3 90b2 ⋅ 7 10b2

630b2

546) 3 5x2 ⋅ 9 5x2

135x2

547) 6 48r2 ⋅ 3 12r2

432r2

548) 10 8n ⋅ 2 10n3

80n25

549) 10 30v ⋅ 4 12v2

240v 10v

550) 6 8a2 ⋅ 7 2a2

168a2

551) 7 3b2 ⋅ 10 15b2

210b25

552) 5 21x2 ⋅ 5 14x3

175x26x

553) 7 3x3 ⋅ 8 4x

112x23

554) 2 14k2 ⋅ 10 28k3

280k22k

555) 3 2 p2 ⋅ 7 20p2

42 p210

556) 8 27x ⋅ 4 70x

96x 210

557) 5 8n3 ⋅ 9 2n3

180n3

558) 4 28m3 ⋅ 5 21m3

280m33

559) 2 8n ⋅ 8 8n2

128n n

560) 2 24r2 ⋅ 10 8r

160r 3r

561) 18x2 ⋅ 3 6x2

18x23

562) 8 12v ⋅ 9 18v2

432v 6v

563) 8 10b3 ⋅ 80b

160b22

564) 4 20x2 ⋅ 7 40x2

560x22

565) 4 54n ⋅ 10 5n

120n 30

566) 5 24k ⋅ 4 30k

240k 5

34

Page 75: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

567) 5 30x2 ⋅ 5 48x

300x 10x

568) 7 60a3 ⋅ 5 45a3

1050a33

569) 3 90x3 ⋅ 8 20x2

720x22x

570) 4 50n3 ⋅ 10 5n2

200n210n

571) 3 35x3 ⋅ 3 12x2

18x2105x

572) 9 28m3 ⋅ 3 14m

378m22

573) 2 8 p ⋅ 6 10p3

48 p25

574) 2 28b2 ⋅ 7 63b2

588b2

575) 6 10n3 ⋅ 9 2n

108n25

576) 10r3 ⋅ 6 10r2

60r2 r

577) 9 14n3 ⋅ 8 12n3

144n342

578) 2 20x3 ⋅ 3 12x2

24x215x

579) 3 24v3 ⋅ 6 40v3

144v315

580) 7 24b3 ⋅ 4 27b

504b22

581) 6 60x2 ⋅ 5 60x

1800x x

582) 10 15x2 ⋅ 4 40x3

400x26x

583) 5 21a2 ⋅ 6 27a3

270a27a

584) 7 20k3 ⋅ 4 15k

280k23

585) 6 12 p3 ⋅ 5 30p3

180 p310

586) 3 15x ⋅ 8 35x2

120x 21x

587) 9 60m3 ⋅ 3 12m2

324m25m

588) 8n3 ⋅ 6 3n

12n26

589) 6 18x ⋅ 9 24x3

648x23

590) 7 14r3 ⋅ 7 54r

294r221

591) 10 24b2 ⋅ 4 54b

1440b b

592) 8 20n3 ⋅ 9 20n2

1440n2 n

35

Page 76: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

593) 9 18v ⋅ 4 12v2

216v 6v

594) 7 42x3 ⋅ 5 21x

735x22

595) 8 42a2 ⋅ 9 15a3

216a270a

596) 5 54n3 ⋅ 6 30n3

540n35

597) 3k3 ⋅ 8 9k

24k23

598) 8 10x3 ⋅ 5 14x3

80x335

599) 3 30x2 ⋅ 2 18x

36x 15x

600) 5 70n ⋅ 6 50n3

300n235

601) 187m3 ⋅ 17 323m2

289m2209m

602) 8 102 p ⋅ 10 27p2

720p 34p

603) 18 95x ⋅ 20 38x2

6840x 10x

604) 15 33n3 ⋅ 14 88n2

4620n26n

605) 3 119b3 ⋅ 4 57b3

12b36783

606) 7 15x3 ⋅ 4 60x

840x2

607) 4 18n2 ⋅ 20 11n3

240n222n

608) 2 247r2 ⋅ 3 133r

114r 91r

609) 14 42a3 ⋅ 18 112a3

7056a36

610) 18 30v2 ⋅ 9 60v2

4860v22

611) 10 187x3 ⋅ 11 221x3

1870x3143

612) 9 16x2 ⋅ 15 36x

3240x x

613) 17 252a2 ⋅ 70a3

714a210a

614) 15 18k3 ⋅ 22k2

90k211k

615) 19 126 p2 ⋅ 14 21p2

5586 p26

616) 20 20x ⋅ 18 10x2

3600x 2x

617) 17 95n3 ⋅ 2 57n

646n215

618) 14 57m2 ⋅ 5 30m3

210m2190m

36

Page 77: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

619) 12 323r ⋅ 11 30r

132r 9690

620) 8 15x ⋅ 13 60x

3120x

621) 2 150b2 ⋅ 11 255b

330b 170b

622) 5 285n3 ⋅ 4 190n2

1900n26n

623) 6 52v3 ⋅ 13 195v

2028v215

624) 19 77x3 ⋅ 12 143x3

2508x391

625) 15 26n ⋅ 2 78n

780n 3

626) 16 6k2 ⋅ 3 10k3

96k215k

627) 15 304a3 ⋅ 12 228a3

27360a33

628) 3 12x3 ⋅ 15 340x3

180x3255

629) 19 8x ⋅ 6 16x2

912x 2x

630) 19 34n3 ⋅ 14 51n

4522n26

631) 16 221m3 ⋅ 11 130m3

2288m3170

632) 9 234x ⋅ 12 39x3

4212x26

633) 4 34n2 ⋅ 20 52n2

160n2442

634) 12 51 p2 ⋅ 4 272p

3264p 3p

635) 3 266b2 ⋅ 5 112b

420b 38b

636) 3 112x3 ⋅ 18 28x3

3024x3

637) 2 126r ⋅ 5 28r3

420r22

638) 18 135n ⋅ 5 210n3

4050n214

639) 12 76v3 ⋅ 8 38v3

3648v32

640) 15 285x2 ⋅ 15 135x2

10125x219

641) 9 126a ⋅ 8 210a

3024a 15

642) 18 55x2 ⋅ 10 88x

3960x 10x

643) 20 300a ⋅ 2 210a2

1200a 70a

644) 14 15 p2 ⋅ 20 120p3

8400p22p

37

Page 78: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

645) 15 65x3 ⋅ 8 126x2

360x2910x

646) 17 154k3 ⋅ 14 11k

2618k214

647) 7 285n ⋅ 12 19n2

1596n 15n

648) 12 51m ⋅ 15 120m

1080m 170

649) 20 285r2 ⋅ 2 57r

2280r 5r

650) 19 45x3 ⋅ 15 104x2

1710x2130x

651) 7 91b2 ⋅ 17 91b

10829b b

652) 9 16n2 ⋅ 6 88n

432n 22n

653) 8 6v3 ⋅ 4 114v

192v219

654) 14 104x3 ⋅ 260x

728x210

655) 6 5n3 ⋅ 11 8n

132n210

656) 20 221a ⋅ 19 182a2

4940a 238a

657) 7 6k ⋅ 2 84k3

84k214

658) 15 252x2 ⋅ 5 98x3

3150x214x

659) 12 130x ⋅ 12 60x

1440x 78

660) 9 98n3 ⋅ 13 182n3

1638n391

661) 6 140m2 ⋅ 5 190m2

300m2266

662) 3 126 p ⋅ 2 84p

252p 6

663) 3 70n3 ⋅ 16 140n2

3360n22n

664) 6 44b2 ⋅ 11 66b3

1452b26b

665) 5 30x ⋅ 2 130x

100x 39

666) 15 140n2 ⋅ 10 133n3

2100n295n

667) 12 66x3 ⋅ 17 132x

13464x22

668) 18 165a ⋅ 6 55a2

5940a 3a

669) 9 133r ⋅ 8 91r2

504r 247r

670) 14 8v ⋅ 6 19v2

168v 38v

38

Page 79: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

671) 11 209x ⋅ 18 57x

3762x 33

672) 17 50x2 ⋅ 5 40x

1700x 5x

673) 3 34n3 ⋅ 40n

12n285

674) 14 171k3 ⋅ 20 171k2

47880k2 k

675) 8 68x ⋅ 9 255x

2448x 15

676) 4 30 p2 ⋅ 14 90p

1680p 3p

677) 13 130r2 ⋅ 14 195r3

11830r26r

678) 2 35n3 ⋅ 9 55n

90n277

679) 14 140m3 ⋅ 5 360m3

4200m314

680) 10 66x3 ⋅ 30x

60x255

681) 14 108n2 ⋅ 15 108n2

22680n2

682) 17 120b ⋅ 19 50b

6460b 15

683) 20 114v3 ⋅ 2 72v3

480v357

684) 16 102x2 ⋅ 20 102x

32640x x

685) 15 48n2 ⋅ 20 102n

3600n 34n

686) 12 28a ⋅ 13 8a3

624a214

687) 9 63k3 ⋅ 6 70k

1134k210

688) 3 70x ⋅ 18 28x2

756x 10x

689) 6 12 p2 ⋅ 11 51p3

396 p217p

690) 18 15n3 ⋅ 14 33n

756n255

691) 3 133m2 ⋅ 10 119m3

210m2323m

692) 13 45n2 ⋅ 17 300n

6630n 15n

693) 21x2 ⋅ 3 30x3

9x270x

694) 12 150b2 ⋅ 3 130b

360b 195b

695) 6 18 p ⋅ 17 48p

1224 p 6

696) 4 85r3 ⋅ 10 5r3

200r317

39

Page 80: Multiplication of radicals - 2 monomials with variables€¦ · 229) 35v3 ⋅ 5v3 230) 7 30x2 ⋅ 12x3 231) 35x2 ⋅ 30x2 232) 6a3 ⋅ 3a3 233) 5 30p2 ⋅ 20p3 234) 7 12n3 ⋅ 3 21n3

697) 16 198x ⋅ 18 400x3

17280x222

698) 4 224n ⋅ 13 182n3

2912n213

699) 13 12a ⋅ 12 3a2

936a a

700) 10 30v3 ⋅ 19 10v

1900v23

40