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8.7 Review Exercises and Sample Exam

Review Exercises

(Assume all variables represent nonnegative numbers.)

Radicals

Simplify.

1. 36

2. 425

3. 16

4. 9

5. 1253

6. 383

7. 1643

8. 5273

9. 40

10. 350

11. 9881

12. 1121

13. 51923

14. 2543

Simplifying Radical Expressions

Simplify.

15. 49x2

16. 25a2b2

17. 75x3y2

18. 200m4n3

19. 18x325y2

20. 108x349y4

21. 216x33

22. 125x6y33

23. 27a7b5c33

24. 120x9y43

Use the distance formula to calculate the distance between the given two points.

25. (5, −8) and (2, −10)

26. (−7, −1) and (−6, 1)

27. (−10, −1) and (0, −5)

28. (5, −1) and (−2, −2)

Adding and Subtracting Radical Expressions

Simplify.

29. 83+33

30. 1210210

31. 143+525362

32. 22ab5ab+7ab2ab

33. 7x(3x+2y)

34. (8yx7xy)(5xy12yx)

35. 45+122075

36. 2432+54232

37. 23x2+45xx27+20x

38. 56a2b+8a2b2224a2ba18b2

39. 5y4x2y(x16y329x2y3)

40. (2b9a2c3a16b2c)(64a2b2c9ba2c)

41. 216x3125xy38x3

42. 128x332x543+32x33

43. 8x3y32x8y3+27x3y3+xy3

44. 27a3b338ab33+a64b3ba3

Multiplying and Dividing Radical Expressions

Multiply.

45. 36

46. (35)2

47. 2(36)

48. (26)2

49. (15)(1+5)

50. (23+5)(3225)

51. 2a234a3

52. 25a2b35a2b23

Divide.

53. 724

54. 104864

55. 98x4y236x2

56. 81x6y738y33

Rationalize the denominator.

57. 27

58. 63

59. 142x

60. 1215

61. 12x23

62. 5a2b5ab23

63. 132

64. 262+6

Rational Exponents

Express in radical form.

65. 71/2

66. 32/3

67. x4/5

68. y3/4

Write as a radical and then simplify.

69. 41/2

70. 501/2

71. 42/3

72. 811/3

73. (14)3/2

74. (1216)1/3

Perform the operations and simplify. Leave answers in exponential form.

75. 31/233/2

76. 21/221/3

77. 43/241/2

78. 93/491/4

79. (36x4y2)1/2

80. (8x6y9)1/3

81. ( a 4/3 a 1/2)2/5

82. (16 x 4/3 y 2)1/2

Solving Radical Equations

Solve.

83. x=5

84. 2x1=3

85. x8+2=5

86. 3x51=11

87. 5x3=2x+15

88. 8x15=x

89. x+41=x1

90. 73x=x3

91. 2(x+1)=2(x+1)

92. x(x+6)=4

93. x(3x+10)3=2

94. 2x2x3+4=5

95. 3(x+4)(x+1)3=5x+373

96. 3x29x+243=(x+2)23

97. y1/23=0

98. y1/3+3=0

99. (x5)1/22=0

100. (2x1)1/35=0

Sample Exam

In problems 1–18, assume all variables represent nonnegative numbers.

1. Simplify.

  1. 100
  2. 100
  3. 100

2. Simplify.

  1. 273
  2. 273
  3. 273

3. 12825

4. 1921253

5. 512x2y3z

6. 250x2y3z53

Perform the operations.

7. 524108+96327

8. 38x2y(x200y18x2y)

9. 2ab(32ab)

10. (x2y)2

Rationalize the denominator.

11. 102x

12. 14xy23

13. 1x+5

14. 232+3

Perform the operations and simplify. Leave answers in exponential form.

15. 22/321/6

16. 104/5101/3

17. (121a4b2)1/2

18. (9 y 1/3 x 6)1/2y1/6

Solve.

19. x7=0

20. 3x+5=1

21. 2x1+2=x

22. 3110x=x4

23. (2x+1)(3x+2)=3(2x+1)

24. x(2x15)3=3

25. The period, T, of a pendulum in seconds is given the formula T=2πL32, where L represents the length in feet. Calculate the length of a pendulum if the period is 1½ seconds. Round off to the nearest tenth.

Review Exercises Answers

1: 6

3: Not a real number

5: 5

7: 1/4

9: 210

11: 729

13: 2033

15: 7x

17: 5xy3x

19: 3x2x5y

21: 6x

23: 3a2bcab23

25: 13

27: 229

29: 113

31: 932

33: 4x2y

35: 533

37: x3+55x

39: 12xyy

41: 4x35xy3

43: 2xy3

45: 32

47: 623

49: −4

51: 2a

53: 32

55: 7xy26

57: 277

59: 72xx

61: 4x32x

63: 3+2

65: 7

67: x45

69: 2

71: 223

73: 1/8

75: 9

77: 4

79: 6x2y

81: a1/3

83: 25

85: 17

87: 6

89: 8

91: −1/2, −1

93: 2/3, −4

95: −5, 5/3

97: 9

99: 9

Sample Exam Answers

1:

  1. 10
  2. Not a real number
  3. −10

3: 825

5: 10xy3yz

7: 146153

9: 6a2b2ba

11: 52xx

13: x5x25

15: 25/6

17: 11a2b

19: 49

21: 5

23: −1/2, 1/3

25: 1.8 feet