Question

Find the cube root of $\frac{125}{216}$

Answer 1

Resolving $125$ and $216$ into prime factors, we get
$125=\underset{}{5\times 5\times 5}$
$\sqrt[3]{3125}=5$
$216=\underset{}{2\times 2\times 2}\times \underset{}{3\times 3\times 3}$
$\therefore \sqrt[3]{3216}=2\times 3$
$\therefore \sqrt[3]{3216}=6$
$\therefore \sqrt[3]{3\frac{125}{216}}=\frac{5}{6}$.