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Elementary Algebra 2e

Review Exercises

Elementary Algebra 2eReview Exercises

Review Exercises

Simplify and Use Square Roots

Simplify Expressions with Square Roots

In the following exercises, simplify.

606.

64 64

607.

144 144

608.

25 25

609.

81 81

610.

−9 −9

611.

−36 −36

612.

64 + 225 64 + 225

613.

64 + 225 64 + 225

Estimate Square Roots

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

614.

28 28

615.

155 155

Approximate Square Roots

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

616.

15 15

617.

57 57

Simplify Variable Expressions with Square Roots

In the following exercises, simplify.

618.

q 2 q 2

619.

64 b 2 64 b 2

620.

121 a 2 121 a 2

621.

225 m 2 n 2 225 m 2 n 2

622.

100 q 2 100 q 2

623.

49 y 2 49 y 2

624.

4 a 2 b 2 4 a 2 b 2

625.

121 c 2 d 2 121 c 2 d 2

Simplify Square Roots

Use the Product Property to Simplify Square Roots

In the following exercises, simplify.

626.

300 300

627.

98 98

628.

x 13 x 13

629.

y 19 y 19

630.

16 m 4 16 m 4

631.

36 n 13 36 n 13

632.

288 m 21 288 m 21

633.

150 n 7 150 n 7

634.

48 r 5 s 4 48 r 5 s 4

635.

108 r 5 s 3 108 r 5 s 3

636.

10 50 5 10 50 5

637.

6 + 72 6 6 + 72 6

Use the Quotient Property to Simplify Square Roots

In the following exercises, simplify.

638.

16 25 16 25

639.

81 36 81 36

640.

x 8 x 4 x 8 x 4

641.

y 6 y 2 y 6 y 2

642.

98 p 6 2 p 2 98 p 6 2 p 2

643.

72 q 8 2 q 4 72 q 8 2 q 4

644.

65 121 65 121

645.

26 169 26 169

646.

64 x 4 25 x 2 64 x 4 25 x 2

647.

36 r 10 16 r 5 36 r 10 16 r 5

648.

48 p 3 q 5 27 p q 48 p 3 q 5 27 p q

649.

12 r 5 s 7 75 r 2 s 12 r 5 s 7 75 r 2 s

Add and Subtract Square Roots

Add and Subtract Like Square Roots

In the following exercises, simplify.

650.

3 2 + 2 3 2 + 2

651.

5 5 + 7 5 5 5 + 7 5

652.

4 y + 4 y 4 y + 4 y

653.

6 m 2 m 6 m 2 m

654.

−3 7 + 2 7 7 −3 7 + 2 7 7

655.

8 13 + 2 3 + 3 13 8 13 + 2 3 + 3 13

656.

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

657.

2 3 r s + 3 r s 5 r s 2 3 r s + 3 r s 5 r s

Add and Subtract Square Roots that Need Simplification

In the following exercises, simplify.

658.

32 + 3 2 32 + 3 2

659.

8 + 3 2 8 + 3 2

660.

72 + 50 72 + 50

661.

48 + 75 48 + 75

662.

3 32 + 98 3 32 + 98

663.

1 3 27 1 8 192 1 3 27 1 8 192

664.

50 y 5 72 y 5 50 y 5 72 y 5

665.

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

Multiply Square Roots

Multiply Square Roots

In the following exercises, simplify.

666.

2 · 20 2 · 20

667.

2 2 · 6 14 2 2 · 6 14

668.

2 m 2 · 20 m 4 2 m 2 · 20 m 4

669.

( 6 2 y ) ( 3 50 y 3 ) ( 6 2 y ) ( 3 50 y 3 )

670.

( 6 3 v 4 ) ( 5 30 v ) ( 6 3 v 4 ) ( 5 30 v )

671.

( 8 ) 2 ( 8 ) 2

672.

( 10 ) 2 ( 10 ) 2

673.

( 2 5 ) ( 5 5 ) ( 2 5 ) ( 5 5 )

674.

( −3 3 ) ( 5 18 ) ( −3 3 ) ( 5 18 )

Use Polynomial Multiplication to Multiply Square Roots

In the following exercises, simplify.

675.

10 ( 2 7 ) 10 ( 2 7 )

676.

3 ( 4 + 12 ) 3 ( 4 + 12 )

677.

( 5 + 2 ) ( 3 2 ) ( 5 + 2 ) ( 3 2 )

678.

( 5 3 7 ) ( 1 2 7 ) ( 5 3 7 ) ( 1 2 7 )

679.

( 1 3 x ) ( 5 + 2 x ) ( 1 3 x ) ( 5 + 2 x )

680.

( 3 + 4 y ) ( 10 y ) ( 3 + 4 y ) ( 10 y )

681.

( 1 + 6 p ) 2 ( 1 + 6 p ) 2

682.

( 2 6 5 ) 2 ( 2 6 5 ) 2

683.

( 3 + 2 7 ) ( 3 2 7 ) ( 3 + 2 7 ) ( 3 2 7 )

684.

( 6 11 ) ( 6 + 11 ) ( 6 11 ) ( 6 + 11 )

Divide Square Roots

Divide Square Roots

In the following exercises, simplify.

685.

75 10 75 10

686.

2 12 6 2 12 6

687.

48 27 48 27

688.

75 x 7 3 x 3 75 x 7 3 x 3

689.

20 y 5 2 y 20 y 5 2 y

690.

98 p 6 q 4 2 p 4 q 8 98 p 6 q 4 2 p 4 q 8

Rationalize a One Term Denominator

In the following exercises, rationalize the denominator.

691.

10 15 10 15

692.

6 6 6 6

693.

5 3 5 5 3 5

694.

10 2 6 10 2 6

695.

3 28 3 28

696.

9 75 9 75

Rationalize a Two Term Denominator

In the following exercises, rationalize the denominator.

697.

4 4 + 27 4 4 + 27

698.

5 2 10 5 2 10

699.

4 2 5 4 2 5

700.

5 4 8 5 4 8

701.

2 p + 3 2 p + 3

702.

x 2 x + 2 x 2 x + 2

Solve Equations with Square Roots

Solve Radical Equations

In the following exercises, solve the equation.

703.

7 z + 1 = 6 7 z + 1 = 6

704.

4 u 2 4 = 0 4 u 2 4 = 0

705.

6 m + 4 5 = 0 6 m + 4 5 = 0

706.

2 u 3 + 2 = 0 2 u 3 + 2 = 0

707.

u 4 + 4 = u u 4 + 4 = u

708.

v 9 + 9 = 0 v 9 + 9 = 0

709.

r 4 r = −10 r 4 r = −10

710.

s 9 s = −9 s 9 s = −9

711.

2 2 x 7 4 = 8 2 2 x 7 4 = 8

712.

2 x = 2 x 7 2 x = 2 x 7

713.

a + 3 = a + 9 a + 3 = a + 9

714.

r + 3 = r + 4 r + 3 = r + 4

715.

u + 2 = u + 5 u + 2 = u + 5

716.

n + 11 1 = n + 4 n + 11 1 = n + 4

717.

y + 5 + 1 = 2 y + 3 y + 5 + 1 = 2 y + 3

Use Square Roots in Applications

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

718.

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=As=A to find the length of each side of his lawn.

719.

A helicopter dropped a package from a height of 900 feet above a stranded hiker. Use the formula t=h4t=h4 to find how many seconds it took for the package to reach the hiker.

720.

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=24ds=24d to find the speed of the car before the brakes were applied.

Higher Roots

Simplify Expressions with Higher Roots

In the following exercises, simplify.

721.


646646
643643

722.


−273−273
−644−644

723.


d99d99
v88v88

724.


a105a105
b273b273

725.


16x8416x84
64y12664y126

726.


128r147128r147
81s24481s244

Use the Product Property to Simplify Expressions with Higher Roots

In the following exercises, simplify.

727.


d99d99

.
728.


543543
12841284

729.


64c8564c85
48d7448d74

730.


343q73343q73
192r96192r96

731.


−5003−5003
−164−164

Use the Quotient Property to Simplify Expressions with Higher Roots

In the following exercises, simplify.

732.

r 10 r 5 5 r 10 r 5 5

733.

w 12 w 2 3 w 12 w 2 3

734.

64 y 8 4 y 5 4 64 y 8 4 y 5 4

735.

54 z 9 2 z 3 3 54 z 9 2 z 3 3

736.

64 a 7 b 2 6 64 a 7 b 2 6

Add and Subtract Higher Roots

In the following exercises, simplify.

737.

4 20 5 2 20 5 4 20 5 2 20 5

738.

4 18 3 + 3 18 3 4 18 3 + 3 18 3

739.

1250 4 162 4 1250 4 162 4

740.

640 c 5 3 −80 c 3 3 640 c 5 3 −80 c 3 3

741.

96 t 8 5 + 486 t 4 5 96 t 8 5 + 486 t 4 5

Rational Exponents

Simplify Expressions with a1na1n

In the following exercises, write as a radical expression.

742.

r 1 8 r 1 8

743.

s 1 10 s 1 10

In the following exercises, write with a rational exponent.

744.

u 5 u 5

745.

v 6 v 6

746.

9 m 3 9 m 3

747.

10 z 6 10 z 6

In the following exercises, simplify.

748.

16 1 4 16 1 4

749.

32 1 5 32 1 5

750.

( −125 ) 1 3 ( −125 ) 1 3

751.

( 125 ) 1 3 ( 125 ) 1 3

752.

( −9 ) 1 2 ( −9 ) 1 2

753.

( 36 ) 1 2 ( 36 ) 1 2

Simplify Expressions with amnamn

In the following exercises, write with a rational exponent.

754.

q 5 3 q 5 3

755.

n 8 5 n 8 5

In the following exercises, simplify.

756.

27 2 3 27 2 3

757.

64 5 2 64 5 2

758.

36 3 2 36 3 2

759.

81 5 2 81 5 2

Use the Laws of Exponents to Simplify Expressions with Rational Exponents

In the following exercises, simplify.

760.

3 4 5 · 3 6 5 3 4 5 · 3 6 5

761.

( x 6 ) 4 3 ( x 6 ) 4 3

762.

z 5 2 z 7 5 z 5 2 z 7 5

763.

( 16 s 9 4 ) 1 4 ( 16 s 9 4 ) 1 4

764.

( m 8 n 12 ) 1 4 ( m 8 n 12 ) 1 4

765.

z 2 3 · z 1 3 z 5 3 z 2 3 · z 1 3 z 5 3

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