Question

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

$110592$

Answer 1

On prime factorising, we get,

$110592=\underset{–}{2\times 2\times 2}\times \underset{–}{2\times 2\times 2}\times \underset{–}{2\times 2\times 2}\times \underset{–}{2\times 3}\times \underset{–}{2\times 3}\times \underset{–}{2\times 3}$

$=8\times 8\times 8\times 6\times 6\times 6$

$=8^3\times 6^3$.

Then, cube root of $110592$ is:

$\sqrt[3]{3110592}=\sqrt[3]{38^3\times 6^3}=8\times 6=48$.

Therefore, $48$ is the required solution.