Maharashtra BoardEnglish MediumSTD 8MathsCubes and Cube Roots2 Marks
Question
Which of the following are perfect cube?1000
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Answer
On factorising 1000 into prime factors, we get
1000 = 2 × 2 × 2 × 5 × 5 × 5
Group the factors in triples of equal factors as:
1000 = {2 × 2 × 2} × {5 × 5 × 5}
It is evident that the prime factors of 1000 can be grouped into triples of equal factors and no factor is left over.
Therefore, 1000 is a perfect cube.
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