Quadratic fields are number fields formed by adjoining the square root of a non-square integer to the rational numbers. These fields can be expressed in the form $$ ext{Q}(\sqrt{d})$$, where $$d$$ is a square-free integer. Quadratic fields are fundamental in algebraic number theory, particularly in the study of Galois theory, as they help illustrate how field extensions and their Galois groups behave.
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