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: 73



Work Step by Step

Rationalize each denominator to obtain: \begin{align*} &=\frac{\sqrt{2}}{\sqrt3}\cdot \frac{\sqrt3}{\sqrt3}+\frac{\sqrt{3}}{\sqrt2}\cdot \frac{\sqrt2}{\sqrt2}\\\\ &=\frac{\sqrt6}{3}+\frac{\sqrt6}{2} \end{align*} Make the expressions similar using their LCD which is $6$ to obtain: \begin{align*} &=\frac{\sqrt6 \cdot 2}{3\cdot 2}+\frac{\sqrt6\cdot 3}{2\cdot 3}\\\\ &=\frac{2\sqrt6}{6}+\frac{3\sqrt6}{6}\\\\ &=\frac{(2+3)\sqrt6}{6}\\\\ &=\frac{5\sqrt6}{6} \end{align*}
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