Question

Which of the following is a perfect square as well as a cube $343,125,81$ or $64$?

• A. $343$
• B. $125$
• C. $81$
• D. $64$

Answer 1

Answer: (D)

$64$

Factorizing the the given numbers to their prime factors, we get,
$\Rightarrow 343=7^3,125=5^3,81=3^4,64=2^6$.

For a number (represented as $x^y$) to be both a perfect cube as well as perfect square, $y$ needs to be a multiple of $6$.
From the given options, only $64$ satisfies this criterion.

Hence, option $D$ is correct.