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 $\displaystyle p, q, r, s$ be integers.

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