Answer
$\frac{\sqrt[3] 3}{2}$
Work Step by Step
$\frac{\sqrt[3] 3}{10} + \sqrt[3] \frac{24}{125}$
Using rules for radicals,
$= \frac{\sqrt[3] 3}{10} +\frac{\sqrt[3] 24}{\sqrt[3] 125}$
$= \frac{\sqrt[3] 3}{10} +\frac{\sqrt[3](3 \times 8) }{\sqrt[3]5^{3}}$
$= \frac{\sqrt[3] 3}{10} +\frac{\sqrt[3](3 \times 2^{3}) }{\sqrt[3]5^{3}}$
$= \frac{\sqrt[3] 3}{10} +\frac{ 2 \sqrt[3]3 }{5}$
$= \frac{\sqrt[3] 3 + 4 \sqrt[3]3 }{10} $
$= \frac{5 \sqrt[3] 3}{10} $
$= \frac{ \sqrt[3] 3}{2} $
