Question

Multiply 137592 by the smallest number so that the product is a perfect cube also, find the cube root of the product​

Answer 1

Answer:

Prime factorising 137592, we get,

137592=2×2×2×3×3×3×7×7×13

=2

3

×3

3

×7

2

×13.

We know, a perfect cube has multiples of 3 as powers of prime factors.

Here, number of 2's is 3, number of 3's is 3, number of 7's is 2 and number of 13's is 1.

So we need to multiply another 7 and 13

2

to the factorization to make 137592 a perfect cube.

Hence, the smallest number by which 137592 must be multiplied to obtain a perfect cube is 7×13

2

=1183.

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