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प्रश्न
Which of the following is perfect cube?
166375
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उत्तर
On factorising 166375 into prime factors, we get:
\[166375 = \left\{ 5 \times 5 \times 5 \right\} \times \left\{ 11 \times 11 \times 11 \right\}\]
Group the factors in triples of equal factors as:
\[166375 = \left\{ 5 \times 5 \times 5 \right\} \times \left\{ 11 \times 11 \times 11 \right\}\]
It is evident that the prime factors of 166375 can be grouped into triples of equal factors and no factor is left over. Therefore, 166375 is a perfect cube.
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