Answer
$2\sqrt[4]{2}+2\sqrt[4]{3}$ or $2(\sqrt[4]{2}+\sqrt[4]{3})$
Work Step by Step
Factor each radicand so that one factor is a perfect fourth power of an integer:
$\sqrt[4]{16\cdot2}+\sqrt[4]{16\cdot3}$
Recall the property (pg. 367):
$\sqrt[n]{a}\cdot\sqrt[n]{b}=\sqrt[n]{ab}$ (if $\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers)
Applying this property, we get:
$\sqrt[4]{16\cdot2}+\sqrt[4]{16\cdot3}$
$=\sqrt[4]{16}\cdot \sqrt[4]{2}+\sqrt[4]{16}\cdot \sqrt[4]{3}$
Recall that $2^4=16$.
Thus,
$\sqrt[4]{16}\cdot \sqrt[4]{2}+\sqrt[4]{16}\cdot \sqrt[4]{3}$
$=2\sqrt[4]{2}+2\sqrt[4]{3}$
Factoring out the $2$ gives:
$2(\sqrt[4]{2}+\sqrt[4]{3})$
