Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.4 The Irrational Numbers - Exercise Set 5.4 - Page 296: 74



Work Step by Step

Rationalize each denominator to obtain: \begin{align*} &=\frac{\sqrt{2}}{\sqrt7}\cdot \frac{\sqrt7}{\sqrt7}+\frac{\sqrt{7}}{\sqrt2}\cdot \frac{\sqrt2}{\sqrt2}\\\\ &=\frac{\sqrt{14}}{7}+\frac{\sqrt{14}}{2} \end{align*} Make the expressions similar using their LCD which is $14$ to obtain: \begin{align*} &=\frac{\sqrt{14} \cdot 2}{7\cdot 2}+\frac{\sqrt{14}\cdot 7}{2\cdot 7}\\\\ &=\frac{2\sqrt{14}}{14}+\frac{7\sqrt{14}}{14}\\\\ &=\frac{(2+7)\sqrt{14}}{14}\\\\ &=\frac{9\sqrt{14}}{14} \end{align*}
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