Maharashtra BoardEnglish MediumSTD 8MathsCubes and Cube Roots1 Mark
Question
Write true (T) or false (F) for the following statement:
392 is a perfect cube.
✓
Answer
False. Solution:
On factorising 392 into prime factors, we got:
392 = 2 × 2 × 2 × 7 × 7
On grouping the factors in triples of equal factors, we get:
392 = {2 × 2 × 2} × 7 × 7
It is evident that the prime factors of 392 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 392 is not a perfect cube.
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