Question

Find the smallest number by which $500$ should be multiplied to make it a perfect cube.

• A. $5$
• B. $10$
• C. $3$
• D. $2$

Answer 1

The correct option is D $2$

Prime factorising $500$, we get,

$500=5\times 5\times 5\times 2\times 2$

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

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

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

So we need to multiply another $2$ to the factorization to make $500$ a perfect cube.

Hence, the smallest number by which $500$ must be multiplied to obtain a perfect cube is $2$.

Therefore, option $D$ is correct.