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In the following exercises, simplify.

Rationalize a One Term Denominator

In the following exercises, rationalize the denominator.

Rationalize a Two Term Denominator

In the following exercises, rationalize the denominator.

4 4 + 27

16 12 3 −11

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2 p + 3

2 p 6 p 3

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Section 9.6 Solve Equations with Square Roots

Solve Radical Equations

In the following exercises, solve the equation.

u 4 + 4 = u

no solution

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r 4 r = −10

13

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2 2 x 7 4 = 8

43 2

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Use Square Roots in Applications

In the following exercises, solve. Round approximations to one decimal place.

A pallet of sod will cover an area of about 600 square feet. Trinh wants to order a pallet of sod to make a square lawn in his backyard. Use the formula s = A to find the length of each side of his lawn.

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A helicopter dropped a package from a height of 900 feet above a stranded hiker. Use the formula t = h 4 to find how many seconds it took for the package to reach the hiker.

7.5 seconds

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Officer Morales measured the skid marks of one of the cars involved in an accident. The length of the skid marks was 245 feet. Use the formula s = 24 d to find the speed of the car before the brakes were applied.

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Section 9.7 Higher Roots

Simplify Expressions with Higher Roots

In the following exercises, simplify.


64 6
64 3

2 4

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d 9 9
v 8 8

d | v |

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16 x 8 4
64 y 12 6

2 x 2 2 y 2

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128 r 14 7
81 s 24 4

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Use the Product Property to Simplify Expressions with Higher Roots

In the following exercises, simplify.


64 c 8 5
48 d 7 4

2 c 2 c 3 5 2 d 3 d 3 4

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343 q 7 3
192 r 9 6

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−500 3
−16 4

−5 4 3 not a real number

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Use the Quotient Property to Simplify Expressions with Higher Roots

In the following exercises, simplify.

Add and Subtract Higher Roots

In the following exercises, simplify.

4 20 5 2 20 5

2 20 5

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640 c 5 3 −80 c 3 3

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96 t 8 5 + 486 t 4 5

2 t 3 t 3 5 + 3 2 t 4 5

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Section 9.8 Rational Exponents

Simplify Expressions with a 1 n

In the following exercises, write as a radical expression.

In the following exercises, write with a rational exponent.

In the following exercises, simplify.

Simplify Expressions with a m n

In the following exercises, write with a rational exponent.

In the following exercises, simplify.

Use the Laws of Exponents to Simplify Expressions with Rational Exponents

In the following exercises, simplify.

( 16 s 9 4 ) 1 4

2 s 9 16

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z 2 3 · z 1 3 z 5 3

z 2

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Practice test

In the following exercises, simplify.

169 m 4 n 2

13 m 2 | n |

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3 13 + 5 2 + 13

4 13 + 5 2

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( 3 6 y ) ( 2 50 y 3 )

180 y 2 3

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( 1 2 q ) 2

1 4 q + 4 q

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81 x 12 4
64 y 18 6

3 x 3 2 y 3

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In the following exercises, rationalize the denominator.

In the following exercises, solve.

3 2 x 3 20 = 7

42

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In the following exercise, solve.

A helicopter flying at an altitude of 600 feet dropped a package to a lifeboat. Use the formula t = h 4 to find how many seconds it took for the package to reach the hiker. Round your answer to the nearest tenth of a second.

6.1 seconds

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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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