Chapter 6.1, Problem 4OE

To determine

To simplify: The given expression and identify if the expression represents the real number.

Answer to Problem 4OE

The simplified value of the given expression is $-\frac{1}{5}$ . The number $-\frac{1}{5}$ is the real number.

Explanation of Solution

Given:

The given expression is

  $-\sqrt{\frac{1}{25}}$

Calculation:

The given expression can be simplified as follows.

  $\begin{array}{l}=-\sqrt{\frac{1}{25}}\\ =-\sqrt{\left(\frac{1}{5}\times \frac{1}{5}\right)}\\ =-\frac{1}{5}\end{array}$

Any number measurable on the number line whether positive, negative, and decimal or in fractions is called the real number.

Here, the number $-\frac{1}{5}$ is the real number.

Therefore, the simplified value of the given expression is $-\frac{1}{5}$ . The number $-\frac{1}{5}$ is the real number.