It comes down to what a fraction actually means. It means the division of a finite quantity into a countable number of pieces. Let's take for example, , a quantity that appears often in trigonometry. We can rationalise the denominator to give , but why would we want to do that?

We need to think about what is actually meant by a fraction, and that is to divide a finite length into a COUNTABLE number of pieces. When written in the form , it is asking you to divide 1 into pieces. This doesn't make sense conceptually, because we can't count . We CAN however, picture a length of (as the diagonal of a unit square), and we can picture it being divided into 2 pieces. That means makes "fractional sense", which is the division of a finite quantity into a countable number of pieces, while does not.