Multiquadratic field
= Multiquadratic field
{title2=$K(\sqrt{a_1},\ldots,\sqrt{a_r})$}
A <field extension> obtained by adjoining finitely many square roots in characteristic different from two. If the classes of $a_1,\ldots,a_r$ are independent in $K^\times/(K^\times)^2$, the extension has degree $2^r$ and <Galois group> $(\mathbb Z/2\mathbb Z)^r$: each square root's sign can be changed independently. The products of distinct square roots form a basis over $K$.