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Cubes and Cube Roots — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsCubes and Cube Roots2 Marks
Question
Which of the following are perfect cube?
456533
✓

Answer

On factorising 456533 into prime factors, we get
456533 = 7 × 7 × 7 × 11 × 11 × 11
Group the factors in triples of equal factors as:
456533 = {7 × 7 × 7} × {11 × 11 × 11}
It is evident that the prime factors of 456533 can be grouped into triples of equal factors and no factor is left over.
Therefore, 456533 is a perfect cube.

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