On the unit group and the $2$-class number of $\mathbb{Q}(\sqrt{2},\sqrt{p},\sqrt{q})$

Let $p\equiv 1(\mathrm{m}\mathrm{o}\mathrm{d}8)$ and $q\equiv 7(\mathrm{m}\mathrm{o}\mathrm{d}8)$ be two prime numbers. The purpose of this paper is to compute the unit group of the fields $\text{KK}=\text{QQ}(\sqrt{2},\sqrt{p},\sqrt{q})$ and give their $2$-class numbers.