Which of the following are perfect cube?4608 - Vidyadip

Question

Which of the following are perfect cube?4608

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Answer

On factorising 3087 into prime factors, we get
4608 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
Group the factors in triples of equal factors as:
4608 = {2 × 2 × 2} × {2 × 2 × 2} × {2 × 2 × 2} × 3 × 3
It is evident that the prime factors of 4608 can be grouped into triples of equal factors and no factor is left over.
Therefore, 4608 is a perfect cube.

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