Question

Which of the following numbers are not perfect cubes?
$\left(iii\right)243$

Answer 1

Check if $243$ is a perfect cube

Prime factors of $243$:

$243=3\times 3\times 3\times 3\times 3$

On grouping the factors of $243$, we get
$243=\{3\times 3\times 3\}\times 3\times 3$

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

Hence, $243$ is not a prefect cube.