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: 3

Answer

$\sqrt{\dfrac{1}{5}}=\dfrac{\sqrt{5}}{5}$

Work Step by Step

$\sqrt{\dfrac{1}{5}}$ Rewrite this fraction as $\dfrac{\sqrt{1}}{\sqrt{5}}$: $\sqrt{\dfrac{1}{5}}=\dfrac{\sqrt{1}}{\sqrt{5}}=\dfrac{1}{\sqrt{5}}=...$ Multiply the fraction by $\dfrac{\sqrt{5}}{\sqrt{5}}$ and simplify: $...=\dfrac{1}{\sqrt{5}}\cdot\dfrac{\sqrt{5}}{\sqrt{5}}=\dfrac{\sqrt{5}}{\sqrt{5^{2}}}=\dfrac{\sqrt{5}}{5}$
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