Hello, I am having difficultly getting started on these two questions. Some hints would be greatly appreciated.

1) Show that $\displaystyle \sqrt{2} \in \mathbb{Q}_7$ by definition (either the infinite series definition or the algebraic definition)

2) Show that a p-adic number $\displaystyle a = \sum_{v=-m}^\infty a_vp^v \in \mathbb{Q}_p$ is a rational number if and only if the sequence of digits is periodic.