I have some numbers $r \in \{-1, 2, \frac{4}{5}, \ldots\}$ and have to find those primes $p$ for which $r$ is a square in $\mathbb{Q}_p$, i. e. is a solution of the equation $X^2 = r$ in $\mathbb{Q}_p$.
How do I do that?
I first thought that I would just try to use Hensel's lemma, but this is an exercise in a chapter about the Hilbert symbol...