Question

Which of the following are perfect cubes ?

ii. $216$

Answer 1

Step: Write the prime factorization of $216$

Prime factorization of $216$:

$\begin{array}{cc}2& 216\\ 2& 108\\ 2& 54\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$

$\therefore 216=\{2\times 2\times 2\}\times \{3\times 3\times 3\}$

Clearly, the prime factors of $216$ can be grouped into triplets of equal factors and no factor is left over.

Hence, $216$ is a perfect cube.