Why eliminate radicals in the denominator? [rationalizing the denominator] Why do all school algebra texts define simplest form for expressions with radicals to not allow a radical in the denominator. For the classic example, $1/\sqrt{3}$ needs to be "simplified" to $\sqrt{3}/3$. 
Is there a mathematical or other reason?
And does the same apply to exponential notation -- are students expected to "simplify" $3^{-1/2}$ to $3^{1/2}/3$ ?

I have had students seem surprised when I told them that I have no preference for $\tan\left(\frac{\pi}{6}\right)$ to be "simplified" to $\frac{\sqrt 3}{3}$, for example.  A high school teacher whom I told this was even more surprised, but no reason was given in defense of requiring the practice.  Nonetheless, to some extent I am glad that high school teachers often tell students that they have to rationalize denominators, because it means that many of them will at least be familiar with the idea when the time comes that "rationalizing" (both denominators and numerators) does serve a purpose in simplifying algebraic expressions, in particular when finding limits in calculus.  
So maybe $\frac{1}{4+\sqrt 3}$ is no less simple than $\frac{4-\sqrt 3}{13}$, but $\frac{h}{\sqrt{x+h}-\sqrt{x}}$ is harder to deal with than $\sqrt{x+h}+\sqrt{x}$ when $h$ goes to $0$, and this comes more easily if you already know how to rationalize denominators with numbers.
