>>14401679The real reason is because back when calculators weren't commonplace, values like 2/sqrt3 were effectively meaningless, whereas rationalising would just tell you to take 2/3rds of sqrt 3, which you'd have written down in some table to as many digits as practical.
No good reason for it to be done nowadays other than giving more intuitive value to figures, for example you have no idea what 6/sqrt7 means until you recall that 7 is close enough to 9 which means that the operation would be close to 6/3 hence giving about 2.
Whereas 6sqrt7/7 is very intuitive at a glance if you have the slightest hint of the value of sqrt7.
This gets even more dramatic with complex values, with things like e/1-i literally having no meaning at all until you make the denominator real.
