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: 68



Work Step by Step

Factor each radicand so that one of the factors is a perfect square to obtain: \begin{align*} &=3\sqrt{9(6)}-2\sqrt{4(6)}-\sqrt{16(6)}+4\sqrt{9(7)}\\ \end{align*} Simplifiy each radical by taking out the square root of each perfect square factor inside the radical sign to obtain: \begin{align*} &=3(3)\sqrt6-2(2)\sqrt6-4\sqrt6+4(3)\sqrt7\\ &=9\sqrt6-4\sqrt6-4\sqrt6+12\sqrt7\\ &=(-94-4)\sqrt6+12\sqrt7\\ &=\sqrt6+12\sqrt7 \end{align*}
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