Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Mid-Chapter Check Point - Page 71: 38

Answer

The required value is $\sqrt{13}-2$

Work Step by Step

Consider the expression, $\left| 2-\sqrt{13} \right|$ The value of $\sqrt{13}>2$. So, the value: $2-\sqrt{13}<0$ According to the definition of absolute value: $\left| x \right|=\left\{ \begin{align} & x\ \ \ \ \ \text{if}\ x\ge 0 \\ & -x\ \ \ \text{if}\ x<0 \\ \end{align} \right.$ Thus, $\begin{align} & \left| 2-\sqrt{13} \right|=-\left( 2-\sqrt{13} \right) \\ & =\sqrt{13}-2 \end{align}$ Therefore, the value of $\left| 2-\sqrt{13} \right|$ is $\sqrt{13}-2$.
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