Multiply following.  Assume that x is positive.

                 (3√x-√y)(2√x-5√y)

Solution               

 (3√x-√y)(2√x-5√y)          =6√x²-15√x√y-2√x√y+5√y²

Note as well that the fourth rule says that we must not have any radicals in the denominator. To get rid of them we will utilize some of the multiplication ideas which we looked at above and the procedure of getting rid of the radicals in denominator is called rationalizing the denominator. Actually that is really what this next set of examples is about. They are actually more examples of rationalizing the denominator instead of simplification examples.