Integer powers and roots · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Integer powers and roots

Mathematics · Number Representation & Place Value · ages 11-14
Name ______________________   Date ____________

  1. What is 2³?

    • 6
    • 8
    • 9

  2. What is 6²?

    • 12
    • 36
    • 64

  3. True or false: 5² means 5 × 2.

    Circle one:   True   False

  4. Work out 5³. Type your answer.

    Answer: ______________

  5. What is ∛64?

    • 4
    • 8
    • 6

  6. Which power of 2 equals 32?

    • 2⁴
    • 2⁵
    • 2⁶

  7. √90 sits between two whole numbers. Type the smaller one.

    Answer: ______________

  8. Mia says √50 equals exactly 7. What's wrong with her answer?

    • 7² = 49, not 50, so √50 is a little more than 7
    • 50 is an even number, so it cannot have a square root
    • She should have said 8 instead of 7
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Integer powers and roots W1-mt_hCVPYlF-7Y-s1

  1. 8 · 2³ means 2 × 2 × 2 = 8. Multiplying 2 by 3 gives 6, which is not the same as cubing.
  2. 36 · 6² means 6 × 6, which is 36. Doubling 6 gives 12, and that's a common mix-up.
  3. False · The small 2 means 5 × 5, using 5 twice in a multiplication. 5 × 2 would just double it.
  4. 125 · 5³ means 5 × 5 × 5, which is 125.
  5. 4 · 4 × 4 × 4 = 64, so the cube root of 64 is 4. 8 is close because 8² = 64, but that's a square, not a cube.
  6. 2⁵ · The powers of 2 go 2, 4, 8, 16, 32, so 2⁵ = 32.
  7. 9 · 9² = 81 and 10² = 100. Since 90 is between them, √90 is between 9 and 10.
  8. 7² = 49, not 50, so √50 is a little more than 7 · Since 7² = 49 and 8² = 64, 50 sits between them, so √50 is close to 7 but not exact.
Worksheet · LightMySky