# How do you solve (sqrt6) - sqrt(3/2)?

Break the fraction under the square root sign into separate square roots, then find the common denominator and eventually get to $\frac{\sqrt{6}}{2}$

#### Explanation:

In order to subtract the fraction from the square root term, we need to have a common denominator.

$\sqrt{6} - \sqrt{\frac{3}{2}}$

The key here is that the one term has a integer under the root sign and the other has a fraction. We can fix that by first taking the fraction under the square root and breaking it down into parts, like this:

$\sqrt{6} - \frac{\sqrt{3}}{\sqrt{2}}$

And now we can multiply the first term by a creative form of 1 (i.e. $= \frac{\sqrt{2}}{\sqrt{2}}$) like so:

$\left(\sqrt{6} \cdot \frac{\sqrt{2}}{\sqrt{2}}\right) - \frac{\sqrt{3}}{\sqrt{2}}$

$= \frac{\sqrt{12}}{\sqrt{2}} - \frac{\sqrt{3}}{\sqrt{2}} = \frac{\sqrt{12} - \sqrt{3}}{\sqrt{2}} = \frac{2 \sqrt{3} - \sqrt{3}}{\sqrt{2}} = \frac{\sqrt{3}}{\sqrt{2}}$

And we can clean this up to get rid of the square root in the denominator:

$\frac{\sqrt{3}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{6}}{2}$