How do you simplify root3(10)/(root3(625))?

Dec 22, 2016

$= \frac{\sqrt[3]{2}}{5}$

Explanation:

Find prime factors and combine the two roots into one.

$\frac{\sqrt[3]{2 \times 5}}{\sqrt[3]{5 \times 5 \times 5 \times 5}} = \sqrt[3]{\frac{2 \times \cancel{5}}{5 \times 5 \times 5 \times 5 \times \cancel{5}}}$

$= \sqrt[3]{\frac{2}{5 \times 5 \times 5}}$

Find the cube root where possible

$= \frac{\sqrt[3]{2}}{5}$