Which of the following number are not perfect cube? 64 - Vidyadip

Question

Which of the following number are not perfect cube?
64

✓

Answer

On factorising 64 into prime factors, we get:
64 = 2 × 2 × 2 × 2 × 2 × 2
On grouping the factors in triples of equal factors, we get:
64 = {2 × 2 × 2} × {2 × 2 × 2}
It is evident that the prime factors of 64 can be grouped into triples of equal factors and no factor is left over. Therefore, 64 is a perfect cube.

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