Question

Find the cube root of each of the following numbers by prime factorisation method: $110592$

• A. $38$
• B. $48$
• C. $58$
• D. none of these
  

Answer 1

Answer: (B)

$48$

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.

Hence, option $B$ is correct.