# How do you simplify sqrt(a^2/b^2)?

Jul 13, 2015

Use the rule $\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}$

#### Explanation:

$= {\sqrt{a}}^{2} / {\sqrt{b}}^{2} = | a \frac{|}{|} b |$

Since ${a}^{2} / {b}^{2}$ is necessarily positive, we must assure that $\frac{a}{b}$ is non-negative as well (that's why the absolute bars).

Or you could have used ${x}^{2} / {y}^{2} = {\left(\frac{x}{y}\right)}^{2}$

$= {\sqrt{\left(\frac{a}{b}\right)}}^{2} = | \frac{a}{b} |$