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 299: 106



Work Step by Step

Rationalize the denominator to obtain: \begin{align*} \sqrt2+\sqrt{\frac{1}{2}}&=\sqrt2 + \sqrt{\frac{1}{2} \cdot \frac{2}{2}}\\ &=\sqrt2 +\sqrt{\frac{2}{4}}\\ &=\sqrt2 + \sqrt{\frac{1}{4} \cdot 2}\\ &=\sqrt2+\frac{1}{2}\sqrt2\\ &=\sqrt2\left(1+\frac{1}{2}\right)\\ &=\sqrt2\left(\frac{3}{2}\right)\\ &=\frac{3\sqrt2}{2} \end{align*}
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