multiplying and dividing radical expressions

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Algebra 2 Lesson 7-2 (Page 368) ALGEBRA 2 LESSON 7-2 Multiplying and Dividing Radical Expressions 7-2

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Multiplying and Dividing Radical Expressions. ALGEBRA 2 LESSON 7-2. Algebra 2 Lesson 7-2 (Page 368). 7-2. Multiplying and Dividing Radical Expressions. ALGEBRA 2 LESSON 7-2. 1. To Multiply Radical Expressions. 7-2. Multiplying and Dividing Radical Expressions. ALGEBRA 2 LESSON 7-2. - PowerPoint PPT Presentation

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Page 1: Multiplying and Dividing Radical Expressions

Algebra 2Lesson 7-2(Page 368)

ALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical Expressions

7-2

Page 2: Multiplying and Dividing Radical Expressions

To Multiply Radical Expressions

ALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical Expressions

7-2

Page 3: Multiplying and Dividing Radical Expressions

If and are real numbers,

Then .

ALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical Expressions

7-2

n a n b

n n na b ab

Page 4: Multiplying and Dividing Radical Expressions

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

Multiply. Simplify if possible.

b. –16 • 4

a. 3 • 12

3 • 12 = 3 • 12 = 36 = 6

The property for multiplying radicals does not apply. –4 is not a real number.

c. –4 • 16

3 3

7-2

3 333–16 • 4 = –16 • 4 = 64 = –4

Page 5: Multiplying and Dividing Radical Expressions

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

Multiply. Simplify if possible.

7-2

. 3 12a 3 3. 3 9b 4 4. 4 4c

  a. 6   b.        c. 36   d.     

  a. –3   b. 3   c. not possible   d. 27

  a. 4   b. –4   c. not possible   d. 2

Page 6: Multiplying and Dividing Radical Expressions

a. 50x5

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

Simplify each expression. Assume all variables are positive.

= 5x2 2x definition of nth root

Factor into perfect squares.50x5 = 52 • 2 • (x2)2 • x

3b. 54n8

33 54n8 = 33 • 2 • (n2)3 • n2 Factor into perfect cubes.

3= 3n2 2n2 definition of nth root

7-2

33= 33(n2)3 • 2n2 n n na • b = ab

= 52 • (x2)2 • 2 • x n n na • b = ab

Page 7: Multiplying and Dividing Radical Expressions

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

Simplify each expression. Assume all variables are positive.

7-2

  a.               b.                  c.                d.               

4. 50a x 3 4. 18b x

  a.               b.                  c.                d.               

Page 8: Multiplying and Dividing Radical Expressions

33 25xy8 • 5x4y3

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

Multiply and simplify . Assume all variables

are positive.

3= 53x3(y3)3 • x2y2 Factor into perfect cubes.

3= 5xy3 x2y2 definition of nth root

7-2

3 3= 53x3(y3)3 • x2y2 n n na • b = ab

25xy8 • 5x4y3 = 25xy8 • 5x4y33 3 3 n n na • b = ab

Page 9: Multiplying and Dividing Radical Expressions

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

Multiply and simplify

Assume all variables are positive.

7-2

3 3 23 7 2 21x x y

  a.           b.            c. 66x 3 y   d. 42xy

Page 10: Multiplying and Dividing Radical Expressions

To Divide Radical Expressions

ALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical Expressions

7-2

Page 11: Multiplying and Dividing Radical Expressions

If and are real numbers,

and ,

then .

ALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical Expressions

7-2

n a n b

n

nn

a a

bb

0b

Page 12: Multiplying and Dividing Radical Expressions

3= 64x7

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

Divide and simplify. Assume all variables are positive.

a.

3= –27

3= (–3)3

= –3

3 –81

33=

b.

3x3

3 192x8

=

192x8

3x

3

=

= 4x2 x3

3= 43(x2)3 • x

7-2

=3 –81

3

Page 13: Multiplying and Dividing Radical Expressions

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

Divide and simplify. Assume all variables are positive.

7-2

Page 14: Multiplying and Dividing Radical Expressions

To of

an expression, rewrite it so there are no

Radicals in any denominators.

ALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical Expressions

7-2

Page 15: Multiplying and Dividing Radical Expressions

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

Rationalize the denominator of each expression. Assume that

all variables are positive.

155=

a.

5

3

7-2

Method 1:

Rewrite as a square root of a fraction.

35

=5

3

= 3 • 55 • 5

Then make the denominator a perfect square.

= 1552

Page 16: Multiplying and Dividing Radical Expressions

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

(continued)

3 • 55 • 5

Multiply the numerator and denominator by 5 so the denominator becomes a whole number.

=3

5

Method 2:

a.

155=

7-2

5

3

Page 17: Multiplying and Dividing Radical Expressions

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

(continued)

b. x5

3x2y

c. 3 54y

x5

3x2y

x5 3x2y

3x2y3x2y

•=

3x7y3x2y

=

x3 3xy3x2y

=

x 3xy3y

=

3 5 • 42y2

4y • 42y2

3 54y

=

Rewrite the fraction so the denominator is a perfect cube.

3 80y2

43y3=

2 10y2

4y3

=

10y2

2y

3=

7-2

Page 18: Multiplying and Dividing Radical Expressions

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

7-2

Page 19: Multiplying and Dividing Radical Expressions

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical ExpressionsALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

The distance d in meters that an object will fall in t seconds is

given by d = 4.9t 2. Express t in terms of d and rationalize the

denominator.

d = 4.9t 2

t 2 =d

4.9

t =d

4.9

10d7

=

d • 1049=

7-2

Page 20: Multiplying and Dividing Radical Expressions

Algebra 2Lesson 7-2(Page 368)

ALGEBRA 2 LESSON 7-2ALGEBRA 2 LESSON 7-2

Multiplying and Dividing Radical ExpressionsMultiplying and Dividing Radical Expressions

7-2