# Chapter 7 - Section 7.4 - Adding and Subtracting Radical Expressions - 7.4 Exercises: 33

$x\sqrt[4]{xy}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $3\sqrt[4]{x^5y}-2x\sqrt[4]{xy} ,$ 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[4]{x^4\cdot xy}-2x\sqrt[4]{xy} \\\\= 3\sqrt[4]{(x)^4\cdot xy}-2x\sqrt[4]{xy} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 3x\sqrt[4]{xy}-2x\sqrt[4]{xy} .\end{array} By combining like radicals, the expression above is equivalent to \begin{array}{l}\require{cancel} (3x-2x)\sqrt[4]{xy} \\\\= x\sqrt[4]{xy} .\end{array}

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