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Elementary Algebra 2e

Review Exercises

Elementary Algebra 2eReview Exercises

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Table of contents
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Use the Language of Algebra
    4. 1.3 Add and Subtract Integers
    5. 1.4 Multiply and Divide Integers
    6. 1.5 Visualize Fractions
    7. 1.6 Add and Subtract Fractions
    8. 1.7 Decimals
    9. 1.8 The Real Numbers
    10. 1.9 Properties of Real Numbers
    11. 1.10 Systems of Measurement
    12. Chapter Review
      1. Key Terms
      2. Key Concepts
    13. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations and Inequalities
    1. Introduction
    2. 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 2.2 Solve Equations using the Division and Multiplication Properties of Equality
    4. 2.3 Solve Equations with Variables and Constants on Both Sides
    5. 2.4 Use a General Strategy to Solve Linear Equations
    6. 2.5 Solve Equations with Fractions or Decimals
    7. 2.6 Solve a Formula for a Specific Variable
    8. 2.7 Solve Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Math Models
    1. Introduction
    2. 3.1 Use a Problem-Solving Strategy
    3. 3.2 Solve Percent Applications
    4. 3.3 Solve Mixture Applications
    5. 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
    6. 3.5 Solve Uniform Motion Applications
    7. 3.6 Solve Applications with Linear Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Graphs
    1. Introduction
    2. 4.1 Use the Rectangular Coordinate System
    3. 4.2 Graph Linear Equations in Two Variables
    4. 4.3 Graph with Intercepts
    5. 4.4 Understand Slope of a Line
    6. 4.5 Use the Slope-Intercept Form of an Equation of a Line
    7. 4.6 Find the Equation of a Line
    8. 4.7 Graphs of Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Systems of Linear Equations
    1. Introduction
    2. 5.1 Solve Systems of Equations by Graphing
    3. 5.2 Solving Systems of Equations by Substitution
    4. 5.3 Solve Systems of Equations by Elimination
    5. 5.4 Solve Applications with Systems of Equations
    6. 5.5 Solve Mixture Applications with Systems of Equations
    7. 5.6 Graphing Systems of Linear Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Polynomials
    1. Introduction
    2. 6.1 Add and Subtract Polynomials
    3. 6.2 Use Multiplication Properties of Exponents
    4. 6.3 Multiply Polynomials
    5. 6.4 Special Products
    6. 6.5 Divide Monomials
    7. 6.6 Divide Polynomials
    8. 6.7 Integer Exponents and Scientific Notation
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Factoring
    1. Introduction
    2. 7.1 Greatest Common Factor and Factor by Grouping
    3. 7.2 Factor Trinomials of the Form x2+bx+c
    4. 7.3 Factor Trinomials of the Form ax2+bx+c
    5. 7.4 Factor Special Products
    6. 7.5 General Strategy for Factoring Polynomials
    7. 7.6 Quadratic Equations
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Rational Expressions and Equations
    1. Introduction
    2. 8.1 Simplify Rational Expressions
    3. 8.2 Multiply and Divide Rational Expressions
    4. 8.3 Add and Subtract Rational Expressions with a Common Denominator
    5. 8.4 Add and Subtract Rational Expressions with Unlike Denominators
    6. 8.5 Simplify Complex Rational Expressions
    7. 8.6 Solve Rational Equations
    8. 8.7 Solve Proportion and Similar Figure Applications
    9. 8.8 Solve Uniform Motion and Work Applications
    10. 8.9 Use Direct and Inverse Variation
    11. Chapter Review
      1. Key Terms
      2. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Roots and Radicals
    1. Introduction
    2. 9.1 Simplify and Use Square Roots
    3. 9.2 Simplify Square Roots
    4. 9.3 Add and Subtract Square Roots
    5. 9.4 Multiply Square Roots
    6. 9.5 Divide Square Roots
    7. 9.6 Solve Equations with Square Roots
    8. 9.7 Higher Roots
    9. 9.8 Rational Exponents
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Quadratic Equations
    1. Introduction
    2. 10.1 Solve Quadratic Equations Using the Square Root Property
    3. 10.2 Solve Quadratic Equations by Completing the Square
    4. 10.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 10.4 Solve Applications Modeled by Quadratic Equations
    6. 10.5 Graphing Quadratic Equations in Two Variables
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  12. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
  13. Index

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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