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 298: 88

Answer

A radical involving square root can be simplified by (i) factoring the radicand (the number inside the radical sign) so that one of the factors is a perfect square; then (ii) extracting out the square root of that perfect square factor. Please refer to the illustration below.

Work Step by Step

A radical involving square root such as $\sqrt{50}$ can be simplified by (i) factoring the radicand (the number inside the radical sign) so that one of the factors is a perfect square; then (ii) extracting out the square root of that perfect square factor. To illustrate: \begin{align*} \sqrt{50}&=\sqrt{25(2)}\\ &=\sqrt{5^2(2)}\\ &=5\sqrt2 \end{align*}
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