Question

Is 292 a perfect cube? if not , find the smallest natural number by which it must be multipiled so that the product is a perfect cube?

Answer 1

292=2*2*71
to make 292 a perfect cube,
it must be multiplied by 10082
which will make it 2943944=2*2*2*71*71*71
Hope it helps!

Answer 2

Solution :

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To Find :

To find whether 292 is a perfect cube or not, To find the smallest natural number by which it must be multipiled so that the product is a perfect cube.

292 = 2 x 2 x 73 , which doesn't have triplet of any prime factors,

Hence, to make it perfect cube, we must make the the prime factors to form triplets,.

292 x 2 x 73 x73 = 2 x 2 x 2 x 73 x 73 x 73

=> Hence, it should be multiplied by 2 x 73 x 73 = 5329 x 2 = 10658.