Question

Which of the following are perfect cubes ?

iii. $243$

Answer 1

Step: Write the prime factorization of $243$

Prime factorization of $243$:

$\begin{array}{cc}3& 243\\ 3& 81\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$

$\Rightarrow 243=\{3\times 3\times 3\}\times 3\times 3$

Clearly, on grouping the factors into triplets of equal factors, we are left with two factors i.e. $3\times 3$

Hence, $243$ is not a perfect cube.