Expert: Steve Holleran - 7/8/2008

Question
rationalize the denominator: 2/((the square root of 3)+(the square root of 2))

Answer
Hi Kalie,

The procedure here is the same no matter what the denominator looks like. You want to multiply the top and bottom by the denominator with the middle sign changed.

Here, the bottom is rt(3) + rt(2), so you want to multiply the top and bottom by [rt(3) - rt(2)]:

  2 / [rt(3) + rt(2)] * [rt(3) - rt(2) / rt(3) - rt(2)]

=  [2rt(3) - 2rt(2)] / rt(3)^2 - rt(2)^2

=  [2rt(3) - 2rt(2)] / 1 = 2rt(3) -2rt(2).

This will work because basically you're multiplying on the bottom the from   (A + B)(A - B) = A^2 - B^2, which is what removes the root.

Hope this was clear enough.
Steve