Quadratic field

A quadratic field is a specific type of number field that is generated by adjoining a square root of a rational number to the field of rational numbers, \(\mathbb{Q}\). More formally, a quadratic field can be expressed in the form: \[ K = \mathbb{Q}(\sqrt{d}) \] where \(d\) is a square-free integer (an integer not divisible by a perfect square greater than 1).