How do you rationalize the denominator and simplify sqrt4/sqrt6?

Aug 31, 2016

$\frac{\sqrt{6}}{3}$

Explanation:

We can start by first realizing that $\sqrt{4}$ is really just $2$. So that makes it $\frac{2}{\sqrt{6}}$.

We can take the next step by getting the square root out of the denominator.

$\left(\frac{2}{\sqrt{6}}\right) \cdot \left(\frac{\sqrt{6}}{\sqrt{6}}\right)$ $=$ $\frac{2 \sqrt{6}}{\sqrt{6}} ^ 2$.

The squared and square root cancel each other out, leaving just $\frac{2 \sqrt{6}}{6}$.

Then you can simplify the $2$ in the numerator and $6$ in the denominator to just get $\frac{1 \sqrt{6}}{3}$, but you would not write the $1$, so $\frac{\sqrt{6}}{3}$.