## Intermediate Algebra (12th Edition)

$5a^2b^2\sqrt{5ab}+5ab\sqrt[3]{ab}$
$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $\sqrt{125a^5b^5}+\sqrt[3]{125a^4b^4} ,$ simplify first each term by expressing the radicand as a factor that is a perfect power of the index. Then, extract the root. $\bf{\text{Solution Details:}}$ 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{25a^4b^4\cdot5ab}+\sqrt[3]{125a^3b^3\cdot ab} \\\\= \sqrt{(5a^2b^2)^2\cdot5ab}+\sqrt[3]{(5ab)^3\cdot ab} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 5a^2b^2\sqrt{5ab}+5ab\sqrt[3]{ab} .\end{array}