Question

Is $243$ a perfect cube? If not, find the smallest number by which $243$ must be multiplied to get a perfect cube.

Answer 1

$243=\underset{}{3\times 3\times 3}\times 3\times 3$
In the above Factorization, $3\times 3$ remains after grouping the $3^{\prime }s$ in triplets. $\therefore 23$ is not a perfect cube.
To make it a perfect cube we multiply it by $3$.
$243\times 3=\underset{}{3\times 3\times 3}\times \underset{}{3\times 3\times 3}$
$729=3^3\times 3^3=(3\times 3{)}^3$
$729=9^3$ which is a perfect cube.
$\therefore 729$ is a perfect cube.