## Intermediate Algebra (12th Edition)

$-11m\sqrt{2}$
$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $3\sqrt{72m^2}-5\sqrt{32m^2}-3\sqrt{18m^2} ,$ 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} 3\sqrt{36m^2\cdot2}-5\sqrt{16m^2\cdot2}-3\sqrt{9m^2\cdot2} \\\\= 3\sqrt{(6m)^2\cdot2}-5\sqrt{(4m)^2\cdot2}-3\sqrt{(3m)^2\cdot2} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 3(6m)\sqrt{2}-5(4m)\sqrt{2}-3(3m)\sqrt{2} \\\\= 18m\sqrt{2}-20m\sqrt{2}-9m\sqrt{2} .\end{array} By combining like radicals, the expression above is equivalent to \begin{array}{l}\require{cancel} (18m-20m-9m)\sqrt{2} \\\\= -11m\sqrt{2} .\end{array}