Chapter A, Problem 3E

Rewrite the expression without using the absolute-value symbol.

5. $\left|\sqrt{5}-5\right|$

To determine

To rewrite: The given expression without using absolute value symbol.

Answer to Problem 3E

The value for the given expression is $5-\sqrt{5}$.

Explanation of Solution

Given:

The expression is $\left|\sqrt{5}-5\right|$.

Calculation:

$\text{The Value of }\left(\sqrt{5}-5\right)<0$.

Therefore, the value becomes,

$\begin{array}{c}\left|\sqrt{5}-5\right|=-\left(\sqrt{5}-5\right)\\ =-\sqrt{5}+5\\ =5-\sqrt{5}\end{array}$

Thus, the value of the given expression is $5-\sqrt{5}$.