\sqrt{ \frac{1}{2} } =  \frac{ \sqrt{1} }{ \sqrt{2} }
sqrt of 1 is 1. 
 \frac{1}{ \sqrt{2} }
rationalizing this
 \frac{1}{ \sqrt{2} }   \frac{ \sqrt{2} }{ \sqrt{2} }

we get 
 \frac{ \sqrt{2} }{2}
why do you have to rationalize square root of two?
well if you do not want, you can. Sometimes its just that teachers dont accept answers which are not rationalized. and rationalizing is somewhat a part of simplifying answers.
so it is still acceptable if ill have the answer one over the square root of two ? :)