Question

Find the cube root of $175616$ by prime factorization method.

• A. $56$
• B. $46$
• C. $36$
• D. $66$

Answer 1

The correct option is A $56$

On prime factorisation of $175616$, we get,

$175616=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 7\times 7\times 7$

$=8\times 8\times 8\times 7\times 7\times 7$

$=8^3\times 7^3$.

Then, cube root of $175616$ is:

$\sqrt[3]{3175616}=\sqrt[3]{38^3\times 7^3}$

$=8\times 7\times$

$=56$

Therefore, option $A$ is correct.