## Intermediate Algebra (12th Edition)

$5\sqrt[4]{2}$
$\bf{\text{Solution Outline:}}$ 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}