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 - Guided Practice for Examples 2, 3 and 4 - Page 268: 12


$\displaystyle \sqrt{\frac{19}{21}}=\frac{\sqrt{399}}{21}$

Work Step by Step

$\sqrt{\frac{19}{21}}\qquad$ ...apply the Quotient Property:$\displaystyle \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ $=\displaystyle \frac{\sqrt{19}}{\sqrt{21}}\qquad$ ...rationalize by multiplying both the numerator and the denominator with $\sqrt{21}$. $=\displaystyle \frac{\sqrt{19}\cdot\sqrt{21}}{\sqrt{21}\cdot\sqrt{21}}\qquad$ ...use the Product Property of square roots:$\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ $=\displaystyle \frac{\sqrt{19\cdot 21}}{\sqrt{21\cdot 21}}\qquad$ ...simplify.($\sqrt{21\cdot 21}=21$). $=\displaystyle \frac{\sqrt{19\cdot 21}}{21}\qquad$ ...simplify. $=\displaystyle \frac{\sqrt{399}}{21}\qquad$ ...we cannot simplify any further. $\sqrt{399}=\sqrt{3\cdot 7\cdot 19}$, no perfect squares.
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