Question

In the following exercises, simplify and rationalize the denominator.

$\sqrt{\frac{19}{175}}$

Short answer

$\frac{\sqrt{133}}{35}$

Step-by-step solution

Step 1. Given information

$\sqrt{\frac{19}{175}}$

Step 2. Rationalize

$$\begin{gathered} \sqrt{\frac{19}{175}} \\ \frac{\sqrt{19}}{\sqrt{175}}\times \frac{\sqrt{175}}{\sqrt{175}} \\ \frac{\sqrt{19}\times 5\sqrt{7}}{175} \\ \frac{\sqrt{133}}{35} \end{gathered}$$