Question

Find the cube root of $592704$ using prime factorization:

• A. $86$
• B. $82$
• C. $84$
• D. $88$

Answer 1

Answer: (C)

$84$

On prime factorizing, we get,

$592704=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 7\times 7\times 7$

$=2^3\times 2^3\times 3^3\times 7^3={84}^3.$

Thus, cube root of $592704$ is:

$\sqrt[3]{3592704}=\sqrt[3]{3{84}^3}=84$.

Therefore, option $C$ is correct.