CLASS 8 MATHS · CUBES AND CUBE ROOTS

Cubes and cube roots

n³ = n × n × n. A perfect cube has prime factors that group into triples.

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Worked examples

Example 1 · level 1

∛729 = ?

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9 × 9 × 9 = 729, so ∛729 = 9.

Answer: 9

Example 2 · level 2

∛3,375 = ?

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15 × 15 × 15 = 3,375, so ∛3,375 = 15.

Answer: 15

Example 3 · level 3

Find the smallest natural number by which 1,372 must be divided so that the result is a perfect cube.

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1,372 = 2 × 2 × 7 × 7 × 7.
2 appears only twice, so it does not make a triple.
Divide by 2² = 4: 1,372 ÷ 4 = 343 = 7³.

Answer: 4