## Intermediate Algebra (12th Edition)

$12xy^4\sqrt{xy}$
$\bf{\text{Solution Outline:}}$ To simplify the given expression, $\sqrt{144x^3y^9} ,$ find a factor of the radicand that is a perfect power of the index. Then extract the root of that factor. Note that all variables are assumed to represent positive real numbers. $\bf{\text{Solution Details:}}$ Expressing the radicand of the expression above with a factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt{144x^2y^8\cdot xy} \\\\= \sqrt{(12xy^4)^2\cdot xy} \\\\= 12xy^4\sqrt{xy} .\end{array}