Question

The smallest number by which 361 must be multiplied so that the product is a perfect cube.

Answer 1

Answer:

Prime factorising 36, we get,

Prime factorising 36, we get,36=2×2×3×3=2

Prime factorising 36, we get,36=2×2×3×3=2 2×3 2

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

We know, a perfect cube has multiples of 3 as powers of prime factors.Here, number of 2's is 2 and number of 3's is 2.

So we need to multiply another 2 and 3 in the factorization to make 36 a perfect cube.

So we need to multiply another 2 and 3 in the factorization to make 36 a perfect cube.Hence, the smallest number by which 36 must be multiplied to obtain a perfect cube is 2×3=6.

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