What is the use of rationalizing the denominator?
In ancient times (when I was a student ) we did arithmetic with pencil and paper.
Now that only hard-cores do arithmetic with pencil and paper, I think of it as a spelling rule. I think of reducing fractions as a spelling rule as well.
What is wrong with writing
Well, really the problem is, that's not how we spell
Rationalizing denominators are similar at the algebra level.
For understanding calculus it becomes quite important to understand why