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( x 8 y 10 ) 1 2
( a 9 b 12 ) 1 3

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( r 8 s 4 ) 1 4
( u 15 v 20 ) 1 5

r 2 s u 3 v 4

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( a 6 b 16 ) 1 2
( j 9 k 6 ) 2 3

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( r 16 s 10 ) 1 2
( u 10 v 5 ) 4 5

r 8 s 5 u 8 v 4

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r 5 2 · r 1 2 r 3 2
s 1 5 · s s 9 5

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a 3 4 · a 1 4 a 10 4
b 2 3 · b b 7 3

a 3 b 4

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c 5 3 · c 1 3 c 2 3
d 3 5 · d d 2 5

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m 7 4 · m 5 4 m 2 4
n 3 7 · n n 4 7

m n 2

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( 64 s 3 5 ) 1 6

2 s 1 10

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( u 12 v 18 ) 1 6

u 2 v 3

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Everyday math

Landscaping Joe wants to have a square garden plot in his backyard. He has enough compost to cover an area of 144 square feet. Simplify 144 1 2 to find the length of each side of his garden.

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Landscaping Elliott wants to make a square patio in his yard. He has enough concrete to pave an area of 242 square feet. Simplify 242 1 2 to find the length of each side of his patio.Round to the nearest tenth of a foot.

15.6 feet

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Gravity While putting up holiday decorations, Bob dropped a decoration from the top of a tree that is 12 feet tall. Simplify 12 1 2 16 1 2 to find how many seconds it took for the decoration to reach the ground. Round to the nearest tenth of a second.

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Gravity An airplane dropped a flare from a height of 1024 feet above a lake. Simplify 1024 1 2 16 1 2 to find how many seconds it took for the flare to reach the water.

8 seconds

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Writing exercises

Show two different algebraic methods to simplify 4 3 2 . Explain all your steps.

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Explain why the expression ( −16 ) 3 2 cannot be evaluated.

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Section 9.1 Simplify and Use Square Roots

Simplify Expressions with Square Roots

In the following exercises, simplify.

Estimate Square Roots

In the following exercises, estimate each square root between two consecutive whole numbers.

Approximate Square Roots

In the following exercises, approximate each square root and round to two decimal places.

Simplify Variable Expressions with Square Roots

In the following exercises, simplify.

Section 9.2 Simplify Square Roots

Use the Product Property to Simplify Square Roots

In the following exercises, simplify.

108 r 5 s 3

6 r 2 s 3 r s

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Use the Quotient Property to Simplify Square Roots

In the following exercises, simplify.

36 r 10 16 r 5

3 r 2 r 2

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12 r 5 s 7 75 r 2 s

2 r s 3 r 5

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Section 9.3 Add and Subtract Square Roots

Add and Subtract Like Square Roots

In the following exercises, simplify.

8 13 + 2 3 + 3 13

11 13 + 2 3

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3 5 x y 5 x y + 3 5 x y

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2 3 r s + 3 r s 5 r s

3 3 r s 5 r s

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Add and Subtract Square Roots that Need Simplification

In the following exercises, simplify.

6 18 n 4 3 8 n 4 + n 2 50

17 n 2 2

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Section 9.4 Multiply Square Roots

Multiply Square Roots

In the following exercises, simplify.

( 6 2 y ) ( 3 50 y 3 )

180 y 2

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Use Polynomial Multiplication to Multiply Square Roots

In the following exercises, simplify.

10 ( 2 7 )

20 10 7

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( 5 + 2 ) ( 3 2 )

13 2 2

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( 5 3 7 ) ( 1 2 7 )

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( 1 3 x ) ( 5 + 2 x )

5 13 x 6 x

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( 3 + 4 y ) ( 10 y )

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( 1 + 6 p ) 2

1 + 12 p + 36 p

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( 3 + 2 7 ) ( 3 2 7 )

−19

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Section 9.5 Divide Square Roots

Divide Square Roots

Practice Key Terms 1

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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