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: 47

Answer

$\sqrt{\dfrac{18}{5}}=\dfrac{6}{\sqrt{10}}$

Work Step by Step

$\sqrt{\dfrac{18}{5}}$ Rewrite this expression as $\dfrac{\sqrt{9\cdot2}}{\sqrt{5}}$ and simplify it: $\sqrt{\dfrac{18}{5}}=\dfrac{\sqrt{9\cdot2}}{\sqrt{5}}=\dfrac{3\sqrt{2}}{\sqrt{5}}=...$ Multiply this expression by $\dfrac{\sqrt{2}}{\sqrt{2}}$ and simplify again if possible: $...=\dfrac{3\sqrt{2}}{\sqrt{5}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{3\sqrt{2^{2}}}{\sqrt{10}}=\dfrac{3(2)}{\sqrt{10}}=\dfrac{6}{\sqrt{10}}$
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