# Help with elementary proof about r in the real numbers

If $$r<0$$, there exists no $$x \in \mathbb{R}$$ such that $$x^2 = r$$.

I'm thinking I need to prove by contradiction assuming there does exist an $$x$$ such that $$x^2=r$$, but I'm having trouble finding the next step. I'm very new at proof writing so any help would be appreciated.

• I would think you would just need to prove the 3 cases (a) x < 0; (b) x = 0; and (c) x > 0. – dan post Apr 19 at 0:04