Now, we’ve discussed numbers having square-roots in some ${\bf Q}_p$ (or ${\bf R}$) and not others. For example, I hope you can check that $\sqrt{-1}\in {\bf Q}_p$ if and only if $p \equiv 1 \mod 4$. But here is the quiz: Which rational numbers have square-roots in ${\bf R}$ and *all* ${\bf Q}_p$?