Chapter 0.2, Problem 28E

To determine

The square root of $-\sqrt{6.25}$ .

Answer to Problem 28E

The square root of $-\sqrt{6.25}$ is $-2.5$ .

Explanation of Solution

Given information:

The number $-\sqrt{6.25}$ .

Formula used:

The square root property which states that square root of any number can be expressed as,

  $\sqrt{{\text{a}}^2}=\text{a}$

Calculation:

Consider the given $-\sqrt{6.25}$ .

Recall the square root property $\sqrt{{\text{a}}^2}=\text{a}$ .

Rewrite $-\sqrt{6.25}$ as,

  $\begin{array}{c}-\sqrt{6.25}=-\sqrt{\frac{625}{100}}\\ =-\sqrt{\frac{25\times 25}{10\times 10}}\\ =-\frac{25}{10}\\ =-2.5\end{array}$

Hence, the square root of $-\sqrt{6.25}$ is $-2.5$ .