(i) Let $K$ be the splitting field of the polynomial $x^{4}-3$ over $\mathbb{Q}$. Describe the field $K$, the Galois group $G=\operatorname{Aut}(K / \mathbb{Q})$, and the action of $G$ on $K$.

(ii) Let $K$ be the splitting field of the polynomial $x^{4}+4 x^{2}+2$ over $\mathbb{Q}$. Describe the field $K$ and determine $\operatorname{Aut}(K / \mathbb{Q})$.