Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 4 Quadratic Functions and Factoring - 4.5 Solve Quadratic Equations by Finding Square Roots - 4.5 Exercises - Skill Practice - Page 269: 13


$\displaystyle \sqrt{\frac{18}{11}}=\frac{3\sqrt{22}}{11}$

Work Step by Step

$\sqrt{\frac{18}{11}}\qquad$ ...apply the Quotient Property:$\displaystyle \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ $=\displaystyle \frac{\sqrt{18}}{\sqrt{11}}\qquad$ ...rewrite 18 as a product of two factors so that one factor is a perfect square. ($18=9\cdot 2$) $=\displaystyle \frac{\sqrt{9\cdot 2}}{\sqrt{11}}\qquad$ ...use the Product Property of square roots in the numerator:$\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ $=\displaystyle \frac{\sqrt{9}\cdot\sqrt{2}}{\sqrt{11}}\qquad$ ...evaluate part of the numerator ($\sqrt{9}=3$) $=\displaystyle \frac{3\sqrt{2}}{\sqrt{11}}\qquad$ ...rationalize the denominator by multyplying both the numerator and the denominator with $\sqrt{11}$. $=\displaystyle \frac{3\sqrt{2}\cdot\sqrt{11}}{\sqrt{11}\cdot\sqrt{11}}\qquad$ ...use the Product Property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ $=\displaystyle \frac{3\sqrt{2\cdot 11}}{\sqrt{11\cdot 11}}\qquad$ ...simplify.($\sqrt{11\cdot 11}=11$). $=\displaystyle \frac{3\sqrt{22}}{11}$
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