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: 71



Work Step by Step

Factor each radicand so that one of the factors is a perfect square to obtain: \begin{align*} &=\frac{\sqrt{16(2)}}{5}+\frac{\sqrt{9(2)}}{7} \end{align*} Simplify each radical to obtain: \begin{align*} &=\frac{4\sqrt2}{5}+\frac{3\sqrt2}{7} \end{align*} Make the expressions similar using their LCD which is $35$ to obtain: \begin{align*} &=\frac{4\sqrt2 \cdot 7}{5\cdot 7} + \frac{3\sqrt2 \cdot 5}{7\cdot 5}\\\\ &=\frac{28\sqrt2}{35}+\frac{15\sqrt2}{35}\\\\ &=\frac{(28+15)\sqrt2}{35}\\\\ &=\frac{43\sqrt2}{35} \end{align*}
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