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प्रश्न
Which of the following is perfect cube?
243
उत्तर
On factorising 243 into prime factors, we get:
\[243 = 3 \times 3 \times 3 \times 3 \times 3\]
Group the factors in triples of equal factors as:
\[243 = \left\{ 3 \times 3 \times 3 \right\} \times 3 \times 3\]
It is evident that the prime factors of 243 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 243 is a not perfect cube.
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