system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5 Why was I taught to always rationalize a denominator?

I was taught to write sin(45) as sqrt2 / 2. Why can't I write 1/sqrt2? It's easier to put into equations the second way.
gpt
It's fine to write it the other way, if you're doing something purely symbolical it's a question of aesthetics.  

However, one reason is that if you approximate sqrt 2 numerically, it's far easier to divide a decimal (non-integer) number by an integer than to divide an integer by a decimal number. This is the case in for example computers, it's much quicker to divide by an integer.