Question

Find the cube root of $438976$ using prime factorization:

• A. $74$
• B. $72$
• C. $76$
• D. $71$

Answer 1

Answer: (C)

$76$

On prime factorising, we get,

$438976$ $=\underset{–}{2\times 2\times 2}\times \underset{–}{2\times 2\times 2}\times \underset{–}{19\times 19\times 19}$

$=2^3\times 2^3\times {19}^3={76}^3$.

Then, cube root of $438976$ is:

$\sqrt[3]{3438976}=\sqrt[3]{3{76}^3}=76$.

Therefore, option $C$ is correct.