# How do you simplify sqrt(7/2)*sqrt(5/3)?

Jul 17, 2017

See a solution process below:

#### Explanation:

Use this rule for radicals to simplify the expression:

$\sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}}$

$\sqrt{\textcolor{red}{\frac{7}{2}}} \cdot \sqrt{\textcolor{b l u e}{\frac{5}{3}}} = \sqrt{\textcolor{red}{\frac{7}{2}} \cdot \textcolor{b l u e}{\frac{5}{3}}} = \sqrt{\frac{35}{6}}$

Or, we can the use this rule of radicals to rewrite the expression:

$\sqrt{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}} = \frac{\sqrt{\textcolor{red}{a}}}{\sqrt{\textcolor{b l u e}{b}}}$

$\sqrt{\frac{\textcolor{red}{35}}{\textcolor{b l u e}{6}}} = \frac{\sqrt{\textcolor{red}{35}}}{\sqrt{\textcolor{b l u e}{6}}}$

If necessary, we can rationalize the denominator using the following process:

$\frac{\sqrt{6}}{\sqrt{6}} \cdot \frac{\sqrt{\textcolor{red}{35}}}{\sqrt{\textcolor{b l u e}{6}}} \implies$

(sqrt(6) * sqrt(color(red)(35)))/(sqrt(6) * sqrt(color(blue)(6)) =>

$\frac{\sqrt{6 \cdot \textcolor{red}{35}}}{6} \implies$

$\frac{\sqrt{210}}{6}$