Exam review Chapter 4
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Identify the index of .
a. / / b. / 7 / c. / 2 / d. / 3____ 2. Identify the radicand of .
a. / 8 / b. / / c. / 6 / d. / 4____ 3. Evaluate .
a. / 1.41 / b. / c. / 16 / d. / 2____ 4. Evaluate .
a. / impossible / b. / –12.8 / c. / 4 / d. / –4____ 5. Evaluate .
a. / b. / 0.7 / c. / 0.007 / d. / 0.49____ 6. Evaluate .
a. / / b. / / c. / / d. /____ 7. Write an equivalent form of 9 as a cube root.
a. / / b. / / c. / / d. /____ 8. Write an equivalent form of 0.4 as a fourth root.
a. / / b. / / c. / / d. /____ 9. Write an equivalent form of as a square root.
a. / / b. / / c. / / d. /____ 10. Which of these roots lies between 3 and 4?
, , ,
a. / / b. / / c. / / d. /____ 11. Evaluate .
a. / 0.0042 / b. / 0.0085 / c. / 0.13 / d. / 0.013____ 12. Evaluate .
a. / 2.1 / b. / 1.3 / c. / 1.8 / d. / –0.1____ 13. Estimate the value of to one decimal place.
a. / –0.3 / b. / 5.7 / c. / 3.4 / d. / 0.9____ 14. Which of these numbers is rational?
, , ,
a. / / b. / / c. / / d. /____ 15. Which of these numbers is irrational?
, , ,
a. / / b. / / c. / / d. /____ 16. Order these numbers from greatest to least: , , , ,
a. / , , , , / c. / , , ,,b. / , , , , / d. / , , , ,
____ 17. Order these numbers from least to greatest: , , , ,
a. / , , , , / c. / , , , ,b. / , , , , / d. / , , , ,
____ 18. Determine which of these numbers is the least.
, , , ,
a. / / b. / / c. / / d. /____ 19. For which number will the fourth root be rational?
256, 27, –81, 40 000
a. / –81 / b. / 256 / c. / 40 000 / d. / 27____ 20. Between which two consecutive integers on a number line would you locate ?
a. / –2 and –3 / b. / 2 and 3 / c. / –1 and –2 / d. / –3 and –4____ 21. Which of these numbers is an integer, but not a whole number?
–9, 0, 1,
a. / –9 / b. / / c. / 0 / d. / 1____ 22. Which of these numbers is a natural number?
9, 0, –1,
a. / 0 / b. / 9 / c. / –1 / d. /____ 23. Which irrational number could be used to represent the hypotenuse of a right triangle with legs 7 cm and 8 cm?
a. / cm / b. / cm / c. / cm / d. / cm____ 24. The area of a square is 64 square inches. What do you know about the square?
a. / Its side length is irrational and its perimeter is rational.b. / Both its side length and its perimeter are irrational.
c. / Its side length is rational and its perimeter is irrational.
d. / Both its side length and its perimeter are rational.
____ 25. Which of these numbers is a whole number, but not a natural number?
0, –3, 1,
a. / 1 / b. / / c. / –3 / d. / 0____ 26. For which number will the fifth root be irrational?
625, 7776, 16 807, –32
a. / –32 / b. / 7776 / c. / 16 807 / d. / 625____ 27. To which set(s) of numbers does belong?
a. / II and III only / b. / I, II and III only / c. / IV only / d. / III only____ 28. Write in simplest form.
a. / b. / / c. / / d. /____ 29. Write in simplest form.
a. / / b. / / c. / / d. /____ 30. Write in simplest form.
a. / / b. / / c. / / d. /____ 31. Write as an entire radical.
a. / / b. / / c. / / d. /____ 32. Write as an entire radical.
a. / / b. / / c. / / d. /____ 33. Write as an entire radical.
a. / / b. / / c. / / d. /____ 34. Write in simplest form.
a. / / b. / c. / / d. /____ 35. Write in simplest form.
a. / / b. / / c. / / d. /____ 36. Write in simplest form.
a. / / b. / / c. / / d. /____ 37. Write as an entire radical.
a. / / b. / / c. / / d. /____ 38. Write as an entire radical.
a. / / b. / / c. / / d. /____ 39. Write as an entire radical.
a. / / b. / / c. / / d. /____ 40. A square has an area of 12 square inches. Determine the side length of the square as a radical in simplest form.
a. / in. / b. / in. / c. / in. / d. / in.____ 41. A cube has a volume of 7290 cm. Determine the edge length of the cube as a radical in simplest form.
a. / cm / b. / cm / c. / cm / d. / cm____ 42. Order these numbers from greatest to least: , , , ,
a. / , , , , / c. / , , , ,b. / , , , , / d. / , , , ,
____ 43. Evaluate without using a calculator.
a. / 8 / b. / 4 / c. / d. / –4____ 44. Evaluate without using a calculator.
a. / 0.29 / b. / 0.5 / c. / 0.05 / d. / 0.125____ 45. Evaluate without using a calculator.
a. / does not exist / b. / –3 / c. / d. / 3____ 46. Evaluate without using a calculator.
a. / / b. / / c. / / d. /____ 47. Write as a radical.
a. / / b. / / c. / / d. /____ 48. Write as a power.
a. / / b. / / c. / / d. /____ 49. Evaluate
a. / 0.010 24 / b. / 0.0256 / c. / 0.1012 / d. / 0.4804____ 50. Evaluate
a. / –27 / c. / 9462.5994...b. / 27 / d. / does not exist
____ 51. Biologists use the formula to estimate the brain mass, b kilograms, of a mammal
with body mass m kilograms. Estimate the brain mass of a mammal with body mass 276 kg.
a. / About 4.24 kg / c. / About 0.42 kgb. / About 253.92 kg / d. / About 9.13 kg
____ 52. A cube has volume 1200 cubic inches. Write the edge length of the cube as a power.
a. / in. / b. / in. / c. / in. / d. / in.____ 53. Write as a radical.
a. / , or / c. / , orb. / , or / d. / , or
____ 54. Evaluate
a. / 18 / c. / 1.741 101...b. / 32 / d. / 40
____ 55. Evaluate
a. / / c. / ...b. / / d. /
____ 56. Evaluate
a. / / b. / does not exist / c. / / d. /____ 57. Arrange these numbers in order from greatest to least.
, , , ,
a. / , , ,, / c. / , , , ,b. / , , ,, / d. / ,, , ,
____ 58. Evaluate without using a calculator.
a. / b. / c. / 9 / d.____ 59. Evaluate
a. / / b. / – / c. / – / d. / –____ 60. Evaluate without using a calculator.
a. / b. / c. / – / d. / –256____ 61. Evaluate without using a calculator.
a. / / b. / / c. / / d. /____ 62. Paleontologists use measurements from fossilized dinosaur tracks
and the formula to estimate the speed at which a dinosaur travelled.
In the formula, v is the speed in metres per second, s is the distance between successive footprints of the same foot, and f is the foot length in metres.
Estimate the speed of the dinosaur when the distance between footprints, s, is 1 m and the foot length, f, is 0.65 m.
a. / About 0.07 m/s / c. / About 0.09 m/sb. / About 0.26 m/s / d. / About 0.43 m/s
____ 63. Evaluate without using a calculator.
a. / b. / c. / – / d. / –____ 64. Evaluate without using a calculator.
a. / / b. / / c. / / d. /____ 65. Evaluate without using a calculator.
a. / / b. / / c. / / d. /____ 66. Evaluate without using a calculator.
a. / / b. / / c. / / d. /____ 67. Evaluate without using a calculator.
a. / / b. / / c. / / d. /____ 68. Which power with a negative exponent is equivalent to ?
a. / / b. / / c. / / d. /____ 69. Which power with a negative exponent is equivalent to ?
a. / / b. / / c. / / d. /____ 70. Given that , what is ?
a. / / b. / –6 / c. / / d.____ 71. Suppose you want $2000 in 3 years. The interest rate for a savings account is 2.8% compounded annually. The money, P dollars, you must invest now is given by the formula . How much must you invest now to have $2000 in 3 years?
a. / $2172.75 / b. / $1836.58 / c. / $1840.99 / d. / $1845.02____ 72. How many times as great as is ?
a. / / b. / / c. / / d. /____ 73. Simplify by writing as a single power.
a. / / b. / / c. / / d. /____ 74. Simplify . Write using powers with positive exponents.
a. / / b. / / c. / / d. /____ 75. Simplify . Write using powers with positive exponents.
a. / / b. / / c. / / d. /____ 76. Simplify .
a. / / b. / / c. / / d. /____ 77. Simplify .
a. / / b. / / c. / / d. /____ 78. Simplify
a. / / b. / / c. / / d. /____ 79. A sphere has volume 350 cubic inches. Determine the radius of the sphere to the nearest inch.
a. / 5 in. / b. / 4 in. / c. / 7 in. / d. / 825 in.____ 80. Evaluate
a. / / b. / / c. / / d. /____ 81. Evaluate
a. / b. / c. / / d. /____ 82. Evaluate
a. / b. / c. / d. /____ 83. Simplify
a. / / b. / / c. / / d. /____ 84. Simplify
a. / / b. / / c. / / d. /____ 85. Simplify
a. / / b. / / c. / / d. /____ 86. Evaluate for and .
a. / / b. / / c. / 531 441 / d. /____ 87. Evaluate for and .
a. / / b. / 72 / c. / / d. /Short Answer
88. Evaluate .
89. Evaluate .
90. Evaluate .
91. Evaluate .
92. Write an equivalent form of 6 as a fifth root.
93. Estimate the value of to one decimal place.
94. Between which 2 consecutive integers on a number line would you locate ?
95. Which of these numbers are rational numbers, but not integers?
, –4, , , 2.4, , 0, ,