Question

Find the smallest number by which the following number must be multiplied to obtain a perfect cube: $243$

Answer 1

Step 1. Solve by factorisation.

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

Step 2. Find the smallest number multiplied to obtain perfect cube

By assorting the factors in triplets of equal factors, $243=(3\times 3\times 3)\times 3\times 3$

Here, $3$ cannot be arranged into triplets of equal factors.

$\therefore$ We will multiply $243$ by $3$ to get a perfect cube.

Hence, the smallest number by which $243$ must be multiplied to obtain a perfect cube is $3$.