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प्रश्न
Which of the following is perfect cube?
64
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उत्तर
On factorising 64 into prime factors, we get
\[64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2\]
Group the factors in triples of equal factors as:
\[64 = \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\}\]
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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