View source for Quadratic irrationality

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A root of a quadratic trinomial with rational coefficients which is irreducible over the field of rational numbers. A quadratic irrationality is representable in the form $a+b\sqrt{d}$, where $a$ and $b$ are rational numbers, $b\ne 0$, and $d$ is an integer which is not a perfect square. A real number $\alpha$ is a quadratic irrationality if and only if it has an infinite periodic [[Continued fraction|continued fraction]] expansion.

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  A.Ya. Khinchin,   "Continued fractions" , Phoenix Sci. Press  (1964)  pp. Chapt. II, §10  (Translated from Russian)</TD></TR></table>