# Chapter 7 - Section 7.5 - Multiplying and Dividing Radical Expressions - 7.5 Exercises - Page 475: 53

$\dfrac{\sqrt{14}}{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To rationalize the given radical expression, $\sqrt{\dfrac{7}{2}} ,$ multiply both the numerator and the denominator by an expression that will make the denominator a perfect power of the index. $\bf{\text{Solution Details:}}$ Multiplying the radicand by an expression equal to $1$ which will make the denominator a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt{\dfrac{7}{2}\cdot\dfrac{2}{2}} \\\\ \sqrt{\dfrac{14}{(2)^2}} .\end{array} Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{\sqrt{14}}{\sqrt{(2)^2}} \\\\= \dfrac{\sqrt{14}}{2} .\end{array}

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