In Calculus it is sometimes necessary to move a radical INTO the denominator in order to determine a limit, so rationalizing all denominators is pointless, IMO. In Precalculus, we begin explaining this to students, and in AP Calculus, we point out that it is not necessary. On the AP exam, any mathematically correct form of the answer is accepted, so I actually encourage them to leave their answers in the form that they get, radical in the bottom or not. Since some textbooks persist in rationalizing the denominators, I just tell the students to check to see if the solutions are equivalent by evaluating both on the calculator (just for checking, not answering the question using a calculator).
On Tue, Aug 28, 2012 at 7:19 AM, allison heyl <email@example.com> wrote: