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: 70



Work Step by Step

Multiply the radicals to obtain: \begin{align*} &=4\sqrt2-8\sqrt{50} \end{align*} Factor the radicand so that one of the factors is a perfect square to obtain: \begin{align*} &=4\sqrt2-8\sqrt{25(2)}\\ \end{align*} Simplifiy the radical by taking out the square root of the perfect square factor inside the radical sign to obtain: \begin{align*} &=4\sqrt2-8(5)\sqrt2\\ &=4\sqrt2-40\sqrt2\\ &=(4-40)\sqrt2\\ &=-36\sqrt2 \end{align*}
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