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 $\sqrt{13}-2$.
