aim: multiply & divide radicals course: adv. alg. & trig. aim: how do we multiply and divide...

Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.

Aim: How do we multiply and divide radicals?

Do Now:

)4)(2( 32 xx

xa • xb = xa + b

))()(4)(2( 32 xx532 88 xx

Divide:

2

35

12

3648

x

xx

xa xb = xa - b

34x x3

Multiply:

Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.

Multiplying Radicals

Multiplying

•Multiply the radicands

4085. ex

•If there are coefficients, find their product, and combine the result with the radical product.

n n nx a y b xy ab

26532563. ex

1215 3303415

n n na b a b rule #1

Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.

Dividing Radicals

Dividing•Divide the radicands

398

72

8

72. ex

•If there are coefficients, find their quotient, and combine the result with the quotient of the radicands. Simplify.

n

nn

x a x a

y by b

n

nn

a a

bb

rule #2

Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.

Model Problems

Simplify:

16

424

4

16

18 96

3 54

22

4

4

16

Note:

616 6

9 6

64 6

3 6

82

16 125 8 5

16

8

125

5

2 25

= 10

Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.

Model Problems

Multiplying a polynomial with a monomial

5 3 2 7( )3 2 5 7 5

Distributive Property

3 2 5 7 5 3 10 35

Rule #1

2 3 6 3( )( ) Multiplying polynomial with a polynomial

FOIL

2 6 2 3 6 3 3 3( ) 12 4 3 3( )

9 4 3

Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.

Model Problems

Simplify.3 32 44 3 16x x

3 32 44 3 16( ) x x

Multiply coefficients

Multiply radicands

3 2 412 16x x

3 612 16x3 612 8 2x Simplify

2 312 2 2x 2 324 2x

Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.

Model Problems

Simplify.3 4 332 2x x

3 4

3

32

2

x

x

3 4

3

1 32

2

x

x

3 3132

2x

3 318 4

2x 31

2 42

x 3 4x

4

31 32

2

x

x

Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.

Model Problems - Find the areas:

square

12

A = e2

A = 1212 1212

212144 units

parallelogram

22

20

A = bhA = 2220

2202 402

Simplify: 1042 1042 1022

104

Aim: Multiply & Divide Radicals Course: Adv. Alg. & Trig.

Application Problem

A city park department rents paddle boats at docks near each entrance to the park. About how far is it to paddle from one dock to the other?

200 m

400 m

Pythagorean Theorem c2 = a2 + b2

Pythagorean Theorem c2 = a2 + b2

c2 = 4002 + 2002

c2 = 160,000 + 40,000c2 = 200,000c = 000,200

000,405 000,405

.52002005 ft .2.447 ft