# How do you simplify sqrt(4/3) -sqrt(3/4)?

Break down the square roots, find common denominators, then combine and get to $\frac{\sqrt{3}}{6}$

#### Explanation:

$\sqrt{\frac{4}{3}} - \sqrt{\frac{3}{4}}$

In order to subtract the two fractions, we need a common denominator. So let's first break the square roots apart and work with the results:

$\frac{2}{\sqrt{3}} - \frac{\sqrt{3}}{2}$

The denominator is going to be $2 \sqrt{3}$, so let's multiply both fractions by forms of 1 to make that happen:

$\frac{2}{\sqrt{3}} \left(1\right) - \frac{\sqrt{3}}{2} \left(1\right)$

$\frac{2}{\sqrt{3}} \left(\frac{2}{2}\right) - \frac{\sqrt{3}}{2} \left(\frac{\sqrt{3}}{\sqrt{3}}\right)$

$\frac{4}{2 \sqrt{3}} - \frac{3}{2 \sqrt{3}}$

$\frac{1}{2 \sqrt{3}}$

And now we'll multiply by another form of 1 to get the square root out of the denominator:

$\frac{1}{2 \sqrt{3}} \left(1\right)$

$\frac{1}{2 \sqrt{3}} \left(\frac{\sqrt{3}}{\sqrt{3}}\right)$

$\frac{\sqrt{3}}{2 \times 3}$

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