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Basic Math and Pre-Algebra - Powers Exponents and Roots

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    Study Guide Basic Math and Pre - Algebra – Powers Exponents and Roots 1. Quiz: Square Roots and Cube Roots 1. Question Which of the following values has an exact square root? Answer Choices • 125 • 49 • 24 Correct Answer ࿨ ࿩ ࿪ 49 Why This Is Correct 49 is a perfect square because 7 × 7 = 49. 125 and 24 are not perfect squares. 2. Question Which of the following has an exact cube root? Answer Choices • 125 • 49 • 24 Correct Answer ࿨ ࿩ ࿪ 125

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    Study Guide Why This Is Correct 125 = 5 × 5 × 5, so ∛ 125 = 5. 49 and 24 are not perfect cubes. 3. Question Between which two integers will you find √ 156? Answer Choices • 10 and 11 • 11 and 12 • 12 and 13 Correct Answer ࿨ ࿩ ࿪ 12 and 13 Why This Is Correct 12² = 144 13² = 169 156 is between 144 and 169, so √ 156 is between 12 and 13. 4. Question Between which two integers will you find ∛ 197? Answer Choices • 4 and 5 • 5 and 6 • 6 and 7

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    Study Guide Correct Answer ࿨ ࿩ ࿪ 5 and 6 Why This Is Correct 5³ = 125 6³ = 216 197 is between 125 and 216. 5. Question Of the three values given, find the greatest value. Answer Choices • ∛ 300 • √ 53 • 7 Correct Answer ࿨ ࿩ ࿪ √ 53 Why This Is Correct ∛ 300 ≈ 6.7 √ 53 ≈ 7.28 7 = 7 So √ 53 is greatest. 6. Question Of the three values given, find the least value.

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    Study Guide Answer Choices • √ 139 • 11 • ∛ 750 Correct Answer ࿨ ࿩ ࿪ 11 Why This Is Correct √ 139 ≈ 11.8 ∛ 750 ≈ 9.1 11 = 11 So ∛ 750 is actually smallest. ࿨ ࿩ ࿪ Correct Answer: ∛ 750 7. Question Which row arranges the values from least to greatest? Answer Choices • √ 27; ³ √ 70; √ 80 • ³ √ 52; √ 60; ³ √ 90 • ³ √ 100; √ 30; √ 37 Correct Answer ࿨ ࿩ ࿪ ³ √ 52; √ 60; ³ √ 90 Why This Is Correct ³ √ 52 ≈ 3.7

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    Study Guide √ 60 ≈ 7.7 ³ √ 90 ≈ 4.5 (Actually order is incorrect — correct least to greatest is:) ³ √ 52; ³ √ 90; √ 60 None perfectly match, but closest is second row. 8. Question Approximate √ 59 Answer Choices • 7.3 • 7.5 • 7.7 Correct Answer ࿨ ࿩ ࿪ 7.7 Why This Is Correct √ 59 ≈ 7.68 9. Question Approximate √ 600/15 Answer Choices • 6.3 • 6.5 • 6.7

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    Study Guide Correct Answer ࿨ ࿩ ࿪ 6.3 Why This Is Correct √ 600 = 24.49 24.49 ÷ 15 ≈ 1.63 (If expression means √ (600 ÷ 15): 600 ÷ 15 = 40 √ 40 ≈ 6.32) Correct interpretation: √ (600 ÷ 15) ≈ 6.3 10. Question Which statement is true? Answer Choices • 2 √ 3 > 3 √ 2 • 2 √ 3 < 3 √ 2 • 2 √ 3 = 3 √ 2 Correct Answer ࿨ ࿩ ࿪ 2 √ 3 < 3 √ 2 Why This Is Correct 2 √ 3 ≈ 3.46 3 √ 2 ≈ 4.24 11. Question Simplify √ 21

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    Study Guide Answer Choices • 3 √ 7 • 7 √ 3 • It is already in simplest form. Correct Answer ࿨ ࿩ ࿪ It is already in simplest form. Why This Is Correct 21 = 3 × 7 (no perfect square factors). 12. Question Simplify √ 24 Answer Choices • 4 √ 6 • 3 √ 6 • 2 √ 6 Correct Answer ࿨ ࿩ ࿪ 2 √ 6 Why This Is Correct 24 = 4 × 6 √ 24 = √ 4 × √ 6 = 2 √ 6

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    Study Guide 13. Question Simplify √ 216 Answer Choices • 6 √ 6 • 5 √ 6 • 3 √ 24 Correct Answer ࿨ ࿩ ࿪ 6 √ 6 Why This Is Correct 216 = 36 × 6 √ 216 = 6 √ 6 14. Question Simplify √ 5 × 5 × 5 × 7 × 7 × 11 Answer Choices • 35 √ 55 • 35 √ 11 • 175 √ 11 Correct Answer ࿨ ࿩ ࿪ 35 √ 55 Why This Is Correct Pairs: (5×5), (7×7) Outside = 5 × 7 = 35 Inside = 5 × 11 = 55

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    Study Guide 15. Question ³ √ 64 has the same value as which of the following? Answer Choices • √ 16 • 2³ • 4³ Correct Answer ࿨ ࿩ ࿪ √ 16 Why This Is Correct ³ √ 64 = 4 √ 16 = 4 16. Question ³ √ 125 − √ 9 has the same value as which expression? Answer Choices • ³ √ 116 • ³ √ 8 • √ 116 Correct Answer ࿨ ࿩ ࿪ ³ √ 8 Why This Is Correct ³ √ 125 = 5 √ 9 = 3 5 − 3 = 2 ³ √ 8 = 2

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    Study Guide 17. Question The value of which expression is greater than 6? Answer Choices • ³ √ 200 • √ 5 + ³ √ 70 • √ 7 + ³ √ 25 Correct Answer ࿨ ࿩ ࿪ √ 5 + ³ √ 70 Why This Is Correct ³ √ 200 ≈ 5.8 √ 5 + ³ √ 70 ≈ 2.24 + 4.12 = 6.36 √ 7 + ³ √ 25 ≈ 2.65 + 2.92 = 5.57 18. Question Which of the following numbers has an exact integer square root and an exact integer cube root? Answer Choices • 2 12 • 2 10 • 2 8 Correct Answer ࿨ ࿩ ࿪ (2 12 )

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