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Elementary Algebra 2e

Review Exercises

Elementary Algebra 2eReview Exercises
  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. Key Terms
    13. Key Concepts
    14. 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. Key Terms
    10. Key Concepts
    11. 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. Key Terms
    9. Key Concepts
    10. 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. Key Terms
    10. Key Concepts
    11. 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. Key Terms
    9. Key Concepts
    10. 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. Key Terms
    10. Key Concepts
    11. 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. Key Terms
    9. Key Concepts
    10. 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. Key Terms
    12. Key Concepts
    13. 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. Key Terms
    11. Key Concepts
    12. 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. Key Terms
    8. Key Concepts
    9. 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.

6464

607.

144144

608.

2525

609.

8181

610.

−9−9

611.

−36−36

612.

64+22564+225

613.

64+22564+225

Estimate Square Roots

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

614.

2828

615.

155155

Approximate Square Roots

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

616.

1515

617.

5757

Simplify Variable Expressions with Square Roots

In the following exercises, simplify.

618.

q2q2

619.

64b264b2

620.

121a2121a2

621.

225m2n2225m2n2

622.

100q2100q2

623.

49y249y2

624.

4a2b24a2b2

625.

121c2d2121c2d2

Simplify Square Roots

Use the Product Property to Simplify Square Roots

In the following exercises, simplify.

626.

300300

627.

9898

628.

x13x13

629.

y19y19

630.

16m416m4

631.

36n1336n13

632.

288m21288m21

633.

150n7150n7

634.

48r5s448r5s4

635.

108r5s3108r5s3

636.

1050510505

637.

6+7266+726

Use the Quotient Property to Simplify Square Roots

In the following exercises, simplify.

638.

16251625

639.

81368136

640.

x8x4x8x4

641.

y6y2y6y2

642.

98p62p298p62p2

643.

72q82q472q82q4

644.

6512165121

645.

2616926169

646.

64x425x264x425x2

647.

36r1016r536r1016r5

648.

48p3q527pq48p3q527pq

649.

12r5s775r2s12r5s775r2s

Add and Subtract Square Roots

Add and Subtract Like Square Roots

In the following exercises, simplify.

650.

32+232+2

651.

55+7555+75

652.

4y+4y4y+4y

653.

6m2m6m2m

654.

−37+277−37+277

655.

813+23+313813+23+313

656.

35xy5xy+35xy35xy5xy+35xy

657.

23rs+3rs5rs23rs+3rs5rs

Add and Subtract Square Roots that Need Simplification

In the following exercises, simplify.

658.

32+3232+32

659.

8+328+32

660.

72+5072+50

661.

48+7548+75

662.

332+98332+98

663.

132718192132718192

664.

50y572y550y572y5

665.

618n438n4+n250618n438n4+n250

Multiply Square Roots

Multiply Square Roots

In the following exercises, simplify.

666.

2·202·20

667.

22·61422·614

668.

2m2·20m42m2·20m4

669.

(62y)(350y3)(62y)(350y3)

670.

(63v4)(530v)(63v4)(530v)

671.

(8)2(8)2

672.

(10)2(10)2

673.

(25)(55)(25)(55)

674.

(−33)(518)(−33)(518)

Use Polynomial Multiplication to Multiply Square Roots

In the following exercises, simplify.

675.

10(27)10(27)

676.

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

677.

(5+2)(32)(5+2)(32)

678.

(537)(127)(537)(127)

679.

(13x)(5+2x)(13x)(5+2x)

680.

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

681.

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

682.

(265)2(265)2

683.

(3+27)(327)(3+27)(327)

684.

(611)(6+11)(611)(6+11)

Divide Square Roots

Divide Square Roots

In the following exercises, simplify.

685.

75107510

686.

21262126

687.

48274827

688.

75x73x375x73x3

689.

20y52y20y52y

690.

98p6q42p4q898p6q42p4q8

Rationalize a One Term Denominator

In the following exercises, rationalize the denominator.

691.

10151015

692.

6666

693.

535535

694.

10261026

695.

328328

696.

975975

Rationalize a Two Term Denominator

In the following exercises, rationalize the denominator.

697.

44+2744+27

698.

52105210

699.

425425

700.

548548

701.

2p+32p+3

702.

x2x+2x2x+2

Solve Equations with Square Roots

Solve Radical Equations

In the following exercises, solve the equation.

703.

7z+1=67z+1=6

704.

4u24=04u24=0

705.

6m+45=06m+45=0

706.

2u3+2=02u3+2=0

707.

u4+4=uu4+4=u

708.

v9+9=0v9+9=0

709.

r4r=−10r4r=−10

710.

s9s=−9s9s=−9

711.

22x74=822x74=8

712.

2x=2x72x=2x7

713.

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

714.

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

715.

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

716.

n+111=n+4n+111=n+4

717.

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

r10r55r10r55

733.

w12w23w12w23

734.

64y84y5464y84y54

735.

54z92z3354z92z33

736.

64a7b2664a7b26

Add and Subtract Higher Roots

In the following exercises, simplify.

737.

4205220542052205

738.

4183+31834183+3183

739.

125041624125041624

740.

640c53−80c33640c53−80c33

741.

96t85+486t4596t85+486t45

Rational Exponents

Simplify Expressions with a1na1n

In the following exercises, write as a radical expression.

742.

r18r18

743.

s110s110

In the following exercises, write with a rational exponent.

744.

u5u5

745.

v6v6

746.

9m39m3

747.

10z610z6

In the following exercises, simplify.

748.

16141614

749.

32153215

750.

(−125)13(−125)13

751.

(125)13(125)13

752.

(−9)12(−9)12

753.

(36)12(36)12

Simplify Expressions with amnamn

In the following exercises, write with a rational exponent.

754.

q53q53

755.

n85n85

In the following exercises, simplify.

756.

27232723

757.

64526452

758.

36323632

759.

81528152

Use the Laws of Exponents to Simplify Expressions with Rational Exponents

In the following exercises, simplify.

760.

345·365345·365

761.

(x6)43(x6)43

762.

z52z75z52z75

763.

(16s94)14(16s94)14

764.

(m8n12)14(m8n12)14

765.

z23·z13z53z23·z13z53

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