Question

Find the cube root of $46656$ by prime factorisation method.

Answer 1

On prime factorising, we get,

$46656=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 3\times 3\times 3$

$=2^3\times 2^3\times 3^3\times 3^3$.

Then, cube root of $46656$ is:

$\sqrt[3]{346656}=\sqrt[3]{32^3\times 2^3\times 3^3\times 3^3}=2\times 2\times 3\times 3=36$.

Therefore, $36$ is the required solution.