Question

Find the cubic root of the following number by prime factorisation method:

$13824$

Answer 1

On prime factorising, we get,

$13824=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3$

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

Then, cube root of $13824$ is:

$\sqrt[3]{313824}=\sqrt[3]{32^3\times 2^3\times 2^3\times 3^3}=2\times 2\times 2\times 3=24$.

Therefore, $24$ is the required solution.