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.

REFERENCES:

Hardy, G. H. "Quadratic Surds." §13 in A Course of Pure Mathematics, 10th ed. Cambridge, England: Cambridge University Press, pp. 20-22, 1967.