Question: The sqrt 2 denominator jumper

The simplification of 1/sqrt(2) is always simplified or unsimplified as the case may be to sqrt(2)/2.  It is a matter of opinion which is simpler I suppose, but throughout mathematics teachings I've always learned cos(45) as 1/sqrt(2) as I'm sure the rest of you all have as well. Yes it is merely aesthetic, but a quirk to see it as sqrt(2)/2

Is the simplification process to get radicals in the numerator rather than the denominator?  I think yes if the answer is numerical in nature.  But here we see in this example using a symbolic approach Maple does the same thing differently 

sqrt(a)/a is in fact simplified to 1/sqrt(a)

And so what is the appeal to have 1/sqrt(2) simplified to sqrt(2)/2?  Better yet I ask why didn't 1/sqrt(a) get simplified to sqrt(a)/a.  Clearly two different logics to the same approach.  Why wasn't the symbolic one applied to the numeric one?  Is there a sim