Question

Simplify: $\sqrt[3]{3\frac{1}{8}\times \frac{125}{64}}$.

• A. $\frac{5}{8}$
• B. $\frac{375}{512}$
• C. $2\frac{1}{2}$
• D. $15\frac{5}{8}$

Answer 1

The correct option is A $\frac{5}{8}$

On prime factorisation of the numbers individually, we get,

$8=\underset{–}{2\times 2\times 2}$

$\Rightarrow \sqrt[3]{3512}=2$.

$125=\underset{–}{5\times 5\times 5}$

$\Rightarrow \sqrt[3]{3125}=5$.

$64=\underset{–}{2\times 2\times 2}\times \underset{–}{2\times 2\times 2}$

$\Rightarrow \sqrt[3]{364}=2\times 2=4$.

Then,

$\sqrt[3]{3\frac{1}{8}\times \frac{125}{64}}=\sqrt[3]{3\frac{1}{8}}\times \sqrt[3]{3\frac{125}{64}}=\frac{\sqrt[3]{31}}{\sqrt[3]{38}}\times \frac{\sqrt[3]{3125}}{\sqrt[3]{364}}$

$=\frac{1}{2}\times \frac{5}{4}=\frac{5}{8}$.

Hence, option $A$ is correct.