Question
Which of the following are perfect cube$?\ 64$
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Answer
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: $64 = \{2 \times 2 \times 2\} \times \{2 \times 2 \times 2\}$ 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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