Quadratic irrational - Definition and Overview

A quadratic irrational number is an irrational number that is the solution to some quadratic equation, and takes on the form

<math>{a+\sqrt{b} \over c}<math>

for integers a, b, c.

Quadratic irrationals are special numbers, especially in relation to continued fractions, where we have the result that all quadratic irrationals have periodic continued fraction forms. For example

<math>\sqrt{3}=1.732\ldots=[1;1,2,1,2,1,2,\ldots]<math>

Example Usage of irrational