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Cubes and Cube Roots — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSCubes and Cube Roots2 Marks
Question
Which of the following are perfect cube$?\ 166375$
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Answer

On factorising $166375$ into prime factors, we get $166375 = 5 × 5 × 5 × 11 × 11 × 11$ Group the factors in triples of equal factors as: $166375 = \{5 × 5 × 5\} × \{11 × 11 × 11\}$ 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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