Question

Simplify the Cube Root of $\frac{64}{125}$?

Answer 1

Step 1: Write both numerators and denominators as a product of its prime factors

We have given $\frac{64}{125}$

$$\begin{gathered} 64=2\times 2\times 2\times 2\times 2\times 2 \\ 125=5\times 5\times 5 \end{gathered}$$

Step 2: Find cube root of both numerator and denominator

$\begin{array}{rcl}\sqrt[3]{\frac{64}{125}}& =& \frac{\sqrt[3]{64}}{\sqrt[3]{125}}\\ & =& \frac{\sqrt[3]{2\times 2\times 2\times 2\times 2\times 2}}{\sqrt[3]{5\times 5\times 5}}\\ & =& \frac{\sqrt[3]{\left(2\times 2\times 2\right)\times \left(2\times 2\times 2\right)}}{\sqrt[3]{5\times 5\times 5}}\\ & =& \frac{2\times 2}{5}\\ & =& \frac{4}{5}\\ & =& 0.8\end{array}$

Hence, the simplified form of the cube root of $\frac{64}{125}$ is $0.8$.