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.
