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

Let p, q, r, s be integers.

If $\displaystyle \sqrt{p}+\sqrt{q}+\sqrt{r}=s$, prove that p, q, r must be perfect squares.

I also asked this on yahoo answers here

Prove 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.