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Core skills · Level 8

Cubes & cube roots

Cube numbers as real cubes, and finding the side again.

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The idea

A cube number makes a cube of blocks. The cube root is the side.

333

Look: 3 layers of 3 × 3: 27 small cubes.

✏️ Your turn!

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  1. 15³ = ?

  2. 2∛1000 = ?

  3. 3∛64 = ?

! Careful!

  • ✗3³ = 9.

    ✓3³ = 3 × 3 × 3 = 27.

  • ✗Pairing primes for a cube root.

    ✓Group in threes.

See the whole lesson on one page

A cube number makes a cube of blocks. The cube root is the side.

3³ = 3 × 3 × 3 = 27, so ∛27 = 3. For big numbers, break into primes and group them in threes.

Think of it like thisA Rubik’s cube is 3 blocks long, 3 wide and 3 high: 27 small cubes. 27 = 3³.

333
3 layers of 3 × 3: 27 small cubes.

Solved together

Question

Find ∛2744.

  1. Break into primes.

    2 × 2 × 2 × 7 × 7 × 7
    2744213722686234374977
  2. Group in threes. Take one from each group.

    2 × 7 = 14

Answer∛2744 = 14.

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Kanakku makes new questions on cubes & cube roots every time. It shows the working and gives a hint when you are stuck.

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