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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.

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

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