How do you prove that p, q and r must be perfect squares?

I recently happened upon a problem that I unfortunately am not able to make any progress on. Here it is:

Let be integers.

If , prove that must be perfect squares.

I also asked this on yahoo answers hereProve that p, q and r must be perfect squares? - Yahoo! Answers .But, I don't think that those solutions address the possibility of having three or two irrational numbers that add up to an integer.

Thank you. Any help with this problem is appreciated.