Question

Find the smallest number which should be multiplied to $15625$ to get a perfect cube.

Answer 1

Prime factorising $15625$, we get,

$15625=5\times 5\times 5\times 5\times 5\times 5$ $=5^6$.

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

Here, number of $5$'s is $6$.

That is, the given number is a perfect cube.

So we need to multiply only $1$ in the factorization to make $15625$ a perfect cube.

Hence, the smallest number by which $15625$ must be multiplied to obtain a perfect cube is $1$.