In mathematics, a biquadratic field is a number field K of a particular kind, which is a Galois extension of the rational number field ℚ with Galois group isomorphic to the Klein four-group.
Biquadratic fields are all obtained by adjoining two square roots.
Therefore in explicit terms they have the form for rational numbers a and b.
There is no loss of generality in taking a and b to be non-zero and square-free integers.
Biquadratic fields are the simplest examples of abelian extensions of ℚ that are not cyclic extensions.