Question

Find the cube root of $13824$ by the method of prime factorization.

• A. $24$
• B. $18$
• C. $12$
• D. $36$

Answer 1

The correct option is A $24$

On prime factorising, we get,

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

$=2^3\times 2^3\times 2^3\times 3^3={24}^3$.

Then, cube root of $13824$ is:

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

Therefore, option $A$ is correct.