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: 69



Work Step by Step

Multiply the radicals to obtain: \begin{align*} 3\sqrt7-5\sqrt{28} \end{align*} Factor the radicand so that one of the factors is a perfect square to obtain: \begin{align*} &=3\sqrt7-5\sqrt{4(7)}\\ \end{align*} Simplifiy the radical by taking out the square root of the perfect square factor inside the radical sign to obtain: \begin{align*} &=3\sqrt7-5(2)\sqrt7\\ &=3\sqrt7-10\sqrt7\\ &=(3-10)\sqrt7\\ &=-7\sqrt7 \end{align*}
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