What is the √2 divided by 2?

Note that 2  = √2 * √2

So

√2 / 2  =  √2 /   [√2 * √2 ]   =    1 / √2

I agree with you CPhill, but isn't a fraction not allowed to have a square root in the denominator?

I think we are supposed to multiply both the numerator and denominator by the square root of 2. 

√2/2 is the final answer. 

But...if we did that....we would just end up with what we started with.....

Besides   1 / √2    is just a number.......there's no "voodoo" associated with having a root in the denominator