Question

Find the cube root of $4096.$

Answer 1

On prime factorising, we get,

$4096=\underset{–}{2\times 2\times 2}\times \underset{–}{2\times 2\times 2}\times \underset{–}{2\times 2\times 2}\times \underset{–}{2\times 2\times 2}$

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

Then, cube root of $4096$ is:

$\sqrt[3]{34096}=\sqrt[3]{32^3\times 2^3\times 2^3\times 2^3}=2\times 2\times 2\times 2=16$.

Therefore, $16$ is the required solution.