# How do you rationalize the denominator and simplify 1/sqrt3?

May 6, 2016

So we want to "rationalize" the denominator by removing the $\sqrt{3}$ from the denominator, and replace it with a whole number.

Well, how can we manipulate the radical into a whole number?

Maybe we can multiply both the top and the bottom by the same number, and rationalize the bottom by doing so?

If you recall, $\sqrt{3} \cdot \sqrt{3} = 3$

So, we can multiply both the top and the bottom by $\frac{\sqrt{3}}{\sqrt{3}}$ to make the bottom into 3!!

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

Since $\frac{\sqrt{3}}{\sqrt{3}} = 0$ we haven't changed the value of anything, so this is good.

We finally have $\frac{\sqrt{3}}{3}$