#### Answer

$5\sqrt[4]{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
\sqrt[4]{32}+3\sqrt[4]{2}
,$ simplify first each term by expressing the radicand as a factor that is a perfect power of the index. Then, extract the root. Finally, combine the like radicals.
$\bf{\text{Solution Details:}}$
Expressing the radicand as an expression that contains a factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt[4]{16\cdot2}+3\sqrt[4]{2}
\\\\
\sqrt[4]{(2)^4\cdot2}+3\sqrt[4]{2}
.\end{array}
Extracting the roots of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
2\sqrt[4]{2}+3\sqrt[4]{2}
.\end{array}
By combining like radicals, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(2+3)\sqrt[4]{2}
\\\\=
5\sqrt[4]{2}
.\end{array}