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 $3^{1/2}/3$ ?
The usual reason I've heard is that dividing by integers is computationally easier -- it's easier to find, say, $(5\sqrt{3})/3$ by computing $5 \times \sqrt{3} \approx 8.66 $ and then dividing by $3$ to get $2.89$ then to find $5/\sqrt{3}$ by dividing $5/1.73$ directly.

The slightly cynical teacher in me wants to say that the reason for demanding no radicals in the denominator is so there is only one right answer to each question, which simplifies grading.
Don't blame your high school teacher 

They are right

$\frac{1}{\sqrt{3}}$ is correctly   "simplified" to $\frac {\sqrt{3}}{3}$. 

Its difficult to find value $\frac{1}{\sqrt{3}}$ as $\sqrt{3}$ is irrational number

Its easy to find value of $\frac {\sqrt{3}}{3}$ as here we are dividing it with 3