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: 72



Work Step by Step

Factor each radicand so that one of the factors is a perfect square to obtain: \begin{align*} &=\frac{\sqrt{9(3)}}{2}+\frac{\sqrt{25(3)}}{7} \end{align*} Simplify each radical to obtain: \begin{align*} &=\frac{3\sqrt3}{2}+\frac{5\sqrt3}{7} \end{align*} Make the expressions similar using their LCD which is $14$ to obtain: \begin{align*} &=\frac{3\sqrt3 \cdot 7}{2\cdot 7} + \frac{5\sqrt3 \cdot 2}{7\cdot 2}\\\\ &=\frac{21\sqrt3}{14}+\frac{10\sqrt3}{14}\\\\ &=\frac{(21+10)\sqrt3}{14}\\\\ &=\frac{31\sqrt3}{14} \end{align*}
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