Question

What is the value of $\sqrt[3]{3(64\times 729)}=$?

• A. $9$
• B. $6$
• C. $36$
• D. $52$

Answer 1

The correct option is C $36$

On prime factorisation of the numbers individually, we get,

$64=\underset{–}{2\times 2\times 2}\times \underset{–}{2\times 2\times 2}$ $=2^3\times 2^3=4^3$.

$729=\underset{–}{3\times 3\times 3}\times \underset{–}{3\times 3\times 3}$ $=3^3\times 3^3=9^3$.

Therefore,

$\sqrt[3]{364\times 729}$ $=\sqrt[3]{34^3\times 9^3}$ $=4\times 9=36$.

Hence, option $C$ is correct.