Question

Find the smallest number by which $675$ must be multiplied to obtain a perfect cube.

Answer 1

Prime factorising $675$, we get,

$675=5\times 5\times 3\times 3\times 3$

$=3^3\times 5^2$.

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

Here, number of $3$'s is $3$ and number of $5$'s is $2$.

So we need to multiply another $5$ in the factorization to make $675$ a perfect cube.

Hence, the smallest number by which $675$ must be multiplied to obtain a perfect cube is $5$.