$\displaystyle \sqrt{p} +\sqrt{q} +\sqrt{z} =s$

Prove that p, q and r must be perfect squares.

Ok so the rule for a square is: $\displaystyle n^2=(n-1)^2+\sqrt{(2n-1)}$

So $\displaystyle p=p-1+\sqrt{2p-1}$ then $\displaystyle p-p=-1+\sqrt{(2p-1)}$ therefore if you square it $\displaystyle 0=1+2p-1$ which goes to $\displaystyle 0=2p$

Where did I go wrong?