objectives: 1.be able to solve a radical equation. 2.be able to solve an equation that contains a...
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![Page 1: Objectives: 1.Be able to solve a radical equation. 2.Be able to solve an equation that contains a rational exponent. Critical Vocabulary: Rational Exponents,](https://reader036.vdocuments.net/reader036/viewer/2022081516/56649e6a5503460f94b68796/html5/thumbnails/1.jpg)
Objectives:1. Be able to solve a radical equation.
2. Be able to solve an equation that contains a rational exponent.
Critical Vocabulary:Rational Exponents, Extraneous Solutions
![Page 2: Objectives: 1.Be able to solve a radical equation. 2.Be able to solve an equation that contains a rational exponent. Critical Vocabulary: Rational Exponents,](https://reader036.vdocuments.net/reader036/viewer/2022081516/56649e6a5503460f94b68796/html5/thumbnails/2.jpg)
I. Solving Radical Equations
1195 xExample 1:
221195 x
12195 x
1305 x
26x
1195 2/1 x
222/1 1195 x
12195 x
1305 x
26x
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I. Solving Radical Equations
Example 2: 8532 x
1332 x
221332 x
16932 x
1662 x
83x
8532 2/1 x
222/1 1332 x
1332 2/1 x
16932 x
1662 x
83x
![Page 4: Objectives: 1.Be able to solve a radical equation. 2.Be able to solve an equation that contains a rational exponent. Critical Vocabulary: Rational Exponents,](https://reader036.vdocuments.net/reader036/viewer/2022081516/56649e6a5503460f94b68796/html5/thumbnails/4.jpg)
I. Solving Radical Equations
Example 3: 3723 x
333 372 x
2772 x
202 x
10x
372 3/1 x
333/1 372 x
2772 x
202 x
10x
![Page 5: Objectives: 1.Be able to solve a radical equation. 2.Be able to solve an equation that contains a rational exponent. Critical Vocabulary: Rational Exponents,](https://reader036.vdocuments.net/reader036/viewer/2022081516/56649e6a5503460f94b68796/html5/thumbnails/5.jpg)
I. Solving Radical Equations
Example 4: 58124 x
3124 x
444 312 x
8112 x
802 x
40x
5812 4/1 x
312 4/1 x
444/1 312 x
8112 x
802 x
40x
This can never happen, therefore the answer is NO SOLUTION and you found an extraneous solution.
![Page 6: Objectives: 1.Be able to solve a radical equation. 2.Be able to solve an equation that contains a rational exponent. Critical Vocabulary: Rational Exponents,](https://reader036.vdocuments.net/reader036/viewer/2022081516/56649e6a5503460f94b68796/html5/thumbnails/6.jpg)
71)2( 4
3
x
II. Solving Rational Exponent Equations
Example 5:
8)2( 4
3
x
3/43/44/3 8)2( x
3 40962 x
3 40962 x
162 x
14x
7124 3 x
824 3 x
44
4 3 82
x
40962 3 x
33 3 40962 x
3 40962 x
3 40962 x
162 x
14x
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23
2 5/1 x
II. Solving Rational Exponent Equations
Example 6:
2
32
3
2
2
3 5/1x
35/1 x
555/1 3x
555/1 3x
243x
23
2 5 x
2
32
3
2
2
3 5 x
35 x
555 3x
243x
![Page 8: Objectives: 1.Be able to solve a radical equation. 2.Be able to solve an equation that contains a rational exponent. Critical Vocabulary: Rational Exponents,](https://reader036.vdocuments.net/reader036/viewer/2022081516/56649e6a5503460f94b68796/html5/thumbnails/8.jpg)
Page 456 #3-21 odds, 23-31(15 problems)
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Objectives:1. Be able to solve a radical equation.
2. Be able to solve an equation that contains a rational exponent.
3. Be able to solve an equation that may contain extraneous solutions.
4. Be able to solve an equation that contains multiple radicals.
Critical Vocabulary:Rational Exponents, Extraneous Solutions
Warm Up: 084 2
3
x 1072 x
![Page 10: Objectives: 1.Be able to solve a radical equation. 2.Be able to solve an equation that contains a rational exponent. Critical Vocabulary: Rational Exponents,](https://reader036.vdocuments.net/reader036/viewer/2022081516/56649e6a5503460f94b68796/html5/thumbnails/10.jpg)
084 2
3
x
WARM UP #1
84 2
3
x
Get the variable and its exponent alone
22
3
x Raise each side to the 2/3 power
3
23
2
2
3
2
x
3 4x
Simplify each side
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1072 x Isolate the root
172 x Get rid of the root
2892 x Solve for “x”
287x
WARM UP #2
![Page 12: Objectives: 1.Be able to solve a radical equation. 2.Be able to solve an equation that contains a rational exponent. Critical Vocabulary: Rational Exponents,](https://reader036.vdocuments.net/reader036/viewer/2022081516/56649e6a5503460f94b68796/html5/thumbnails/12.jpg)
III. Solving Equations with Extraneous Solutions
Isolate the root
Get rid of the root
Solve for “x”
272 xx
272 xx
4472 2 xxx
320 2 xx320 2 xx
)1)(3(0 xx3x 1x Check for extraneous
solutions
![Page 13: Objectives: 1.Be able to solve a radical equation. 2.Be able to solve an equation that contains a rational exponent. Critical Vocabulary: Rational Exponents,](https://reader036.vdocuments.net/reader036/viewer/2022081516/56649e6a5503460f94b68796/html5/thumbnails/13.jpg)
Get rid of the root
Solve for “x”
Check for extraneous solutions
xx 24 xxx 21682
016102 xx016102 xx0)2)(8( xx
8x 2x
III. Solving Equations with Extraneous Solutions
![Page 14: Objectives: 1.Be able to solve a radical equation. 2.Be able to solve an equation that contains a rational exponent. Critical Vocabulary: Rational Exponents,](https://reader036.vdocuments.net/reader036/viewer/2022081516/56649e6a5503460f94b68796/html5/thumbnails/14.jpg)
IV. Solving Equations with Multiple Radicals
Move the root
Square Both Sides
Isolate the Root
1352 xx
23252 xxx1352 xx
32
3
x
xSquare Both Sides
Solve for “x”
124962 xxx021102 xx0)3)(7( xx
7x 3xCheck for Extraneous
Solutions
34
962
xxx
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Page 457 #34-43, 45-52