Question

Evaluate:
$\sqrt[3]{\frac{125}{216}}$

Answer 1

$\sqrt[3]{\frac{125}{216}}$
By prime factorisation:



$\sqrt[3]{\frac{125}{216}}$ = $\frac{\sqrt[3]{5\times 5\times 5}}{\sqrt[3]{\left(2\times 2\times 2\right)\times \left(3\times 3\times 3\right)}}$ = $\frac{\sqrt[3]{5\times 5\times 5}}{\sqrt[3]{\left(6\times 6\times 6\right)}}=\frac{5}{6}$

∴ $\sqrt[3]{\frac{125}{216}}$ = $\frac{5}{6}$