Question

Which of the following numbers is a perfect cube as well as a perfect square?

• A. $125$
• B. $625$
• C. $729$
• D. $1000$

Answer 1

The correct option is C $729$

Expressing the given numbers in terms of their prime factors, we have,
$125=5^3$

$625=5^4$

$729=3^6$

$1000=2^3\times 5^3$.

For number to be both perfect cube and a perfect square one of the exponents must be a multiple of $6$ (LCM of $2,3$).

Of the above numbers only $729$ satisfies this criterion.

Hence, option $C$ is correct.