It is a tradition in elementary schools to transform a quotient like 1/√2 into another one in which the square root sign does not appear in the denominator. As far as we are concerned, doing this is not particularly useful in general. It may be useful in special cases, but neither more nor less than other manipulations with quotients, to be determined ad hoc as the need arises. Actually, in many cases it is useful to have the square root in the denominator.
Serge Lang, Basic Mathematics.