# How do you find the set in which the real number -sqrt(0.0625) belongs?

Mar 9, 2017

$- \sqrt{0.0625}$ is a rational number.

#### Explanation:

Note that:

$0.0625 = \frac{0.125}{2} = \frac{0.25}{4} = \frac{0.5}{8} = \frac{1}{16} = {\left(\frac{1}{4}\right)}^{2}$

So:

$\sqrt{0.0625} = \sqrt{{\left(\frac{1}{4}\right)}^{2}} = \frac{1}{4}$

So:

$- \sqrt{0.0625} = - \frac{1}{4}$

This is a rational number, since it is expressible in the form $\frac{p}{q}$ for integers $p , q$ with $q \ne 0$. For example: $p = - 1$ and $q = 4$.