How do you rationalize the denominator sqrt(x/5)?

Apr 17, 2018

The rationalized fraction is $\frac{\sqrt{5 x}}{5}$.

Explanation:

$\textcolor{w h i t e}{=} \sqrt{\frac{x}{5}}$

$= \frac{\sqrt{x}}{\sqrt{5}}$

Then multiply the top and bottom by $\sqrt{5}$:

$= \frac{\sqrt{x}}{\sqrt{5}} \textcolor{red}{\cdot \frac{\sqrt{5}}{\sqrt{5}}}$

$= \frac{\sqrt{x} \cdot \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}}$

$= \frac{\sqrt{x} \cdot \sqrt{5}}{{\left(\sqrt{5}\right)}^{2}}$

$= \frac{\sqrt{x} \cdot \sqrt{5}}{5}$

$= \frac{\sqrt{x \cdot 5}}{5}$

$= \frac{\sqrt{5 x}}{5}$

That's it. Hope this helped!