Maths worksheets · lesson 59 of 64 · free

Cubes and cube roots — Maths worksheet

The cube of a number is the number used three times in a product: 14³ = 14 × 14 × 14 = 2744, and the cube root goes back: ∛2744 = 14. A perfect cube has all its prime factors in groups of three, so 54 = 2 × 3 × 3 × 3 needs 2 × 2 = 4 more to become a cube (216). A cube of edge a has volume a³.

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The method

Threes make cubes — “a perfect cube has every prime factor in groups of three”

  1. Cube: n × n × n. Cube root: the number that, used three times, gives the cube.
  2. Units digits: 1→1, 2→8, 3→7, 4→4, 5→5, 6→6, 7→3, 8→2, 9→9, 0→0 — use them to guess cube roots.
  3. Make a perfect cube: break into primes; multiply by what completes each group of three (or divide by what is left over).
  4. A big cube of edge a cut into small cubes of edge b gives (a ÷ b)³ small cubes.

Use it for: Volumes of boxes and tanks, stacking cubes, and the cubes and cube roots chapter of Class 8 maths.

Worked example: What is ∛2744? → 14

  1. 10³ = 1000 and 20³ = 8000, so the root is between 10 and 20; 2744 ends in 4, so the root ends in 4. Try 14: 14 × 14 × 14 = 2744.
  2. ∛2744 = 14.

Check: 14 × 14 = 196 and 196 × 14 = 2744 ✓

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🏁 Lesson 59 test

20 sums. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ Class 8 Maths Worksheet: Cubes and Cube Roots

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