Quadratic Surd
A number of the form 
, where 
is a positive rational
number which is not the square of another rational number is called a pure quadratic
surd. A number of the form 
, where
is rational and 
is a pure
quadratic surd is sometimes called a mixed quadratic surd (Hardy 1967, p. 20).
Quadratic surds are sometimes also called quadratic irrationals.
In 1770, Lagrange proved that any quadratic surd has a regular continued fraction which is periodic after some point. This result is known as Lagrange's continued fraction theorem.
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