# Why is it so important to rationalize radicals in the denominator?

Even in my second semester of calc I have yet to see a situation where the extra step made any sense why is it important to write $$\frac{3\sqrt{13}}{13}$$ instead of leaving $$\frac{3}{\sqrt{13}}$$. Its not a big deal but even my profs say its not that important so it has peaked my curiosity.

For me I don't see it as that important, except perhaps it allows you to see the approximate value easier in *some* cases. For example, we know that sqrt(2) is about 1.4142. So the reciprocal 1/sqrt(2) will be 1/1.4142, not that easy to see what the value is compared to sqrt(2)/2 which is about 1.4142/2 = 0.7071.

We have a discussion at https://www.physicsforums.com/showthread.php?t=130776

CRGreathouse