Answer
$(x+2)\sqrt[4]{2x}$
Work Step by Step
Simplify each radical by factoring the radicand such that one of the factors is a fourth power:
$\sqrt[4]{32x}+\sqrt[4]{2x^5}\\
=\sqrt[4]{16\cdot 2x}+\sqrt[4]{x^4\cdot 2x}\\
=\sqrt[4]{2^4\cdot 2x}+\sqrt[4]{x^4\cdot 2x}$
Use the rule $\sqrt[n]{a\cdot b}=\sqrt[n]{a} \cdot \sqrt[n]{b}$ then simplify:
$=\sqrt[4]{2^4}\cdot \sqrt[4]{2x}+\sqrt[4]{x^4}\cdot \sqrt[4]{2x}$
$=2\cdot \sqrt[4]{2x}+x\cdot\sqrt[4]{2x}$
$=2\sqrt[4]{2x}+x\sqrt[4]{2x}$
Factor out $\sqrt[4]{2x}$.
$=\sqrt[4]{2x}(2+x)$
$=(2+x)\sqrt[4]{2x}$
$=(x+2)\sqrt[4]{2x}$
Hence, the correct answer is $(x+2)\sqrt[4]{2x}$.
