Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.5 - Rationalizing Numerators and Denominators of Radical Expressions - Exercise Set: 22

Answer

$\sqrt{\dfrac{11y}{45}}=\dfrac{\sqrt{55y}}{15}$

Work Step by Step

$\sqrt{\dfrac{11y}{45}}$ Rewrite this expression as $\dfrac{\sqrt{11y}}{\sqrt{9\cdot5}}$ and simplify it: $\sqrt{\dfrac{11y}{45}}=\dfrac{\sqrt{11y}}{\sqrt{9\cdot5}}=\dfrac{\sqrt{11y}}{3\sqrt{5}}=...$ Multiply the fraction by $\dfrac{\sqrt{5}}{\sqrt{5}}$ and simplify again: $...=\dfrac{\sqrt{11y}}{3\sqrt{5}}\cdot\dfrac{\sqrt{5}}{\sqrt{5}}=\dfrac{\sqrt{55y}}{3\sqrt{5^{2}}}=\dfrac{\sqrt{55y}}{3(5)}=\dfrac{\sqrt{55y}}{15}$
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