# Chapter 7 - Section 7.4 - Adding and Subtracting Radical Expressions - 7.4 Exercises - Page 466: 18

$3\sqrt{6}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $5\sqrt{54}-2\sqrt{24}-2\sqrt{96} ,$ 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} 5\sqrt{9\cdot6}-2\sqrt{4\cdot6}-2\sqrt{16\cdot6} \\\\= 5\sqrt{(3)^2\cdot6}-2\sqrt{(2)^2\cdot6}-2\sqrt{(4)^2\cdot6} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 5(3)\sqrt{6}-2(2)\sqrt{6}-2(4)\sqrt{6} \\\\= 15\sqrt{6}-4\sqrt{6}-8\sqrt{6} .\end{array} By combining like radicals, the expression above is equivalent to \begin{array}{l}\require{cancel} (15-4-8)\sqrt{6} \\\\= 3\sqrt{6} .\end{array}

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