If $p\equiv 1 \, \mathrm {mod} \, 4$ is a prime, then $\sqrt p \in\mathbb Q(\xi_p)$ where $\xi_p$ is the $p$-th root of unity.
How to prove the above claim?
(I need this fact to prove quadratic reciprocity law in J.S. Miline's Algebraic Number Theory on p 143, it metions $p$ is the only prime ramifying in $\mathbb Q [\sqrt p]$, I'm not sure wether it helps or not.)