Quadratic Surd

A number of the form +/-sqrt(a), where a 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 a+/-sqrt(b), where a is rational and sqrt(b) 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.

See also

Continued Fraction, Lagrange's Continued Fraction Theorem, Minkowski's Question Mark Function, nth Root, Quadratic, Square Root, Surd

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

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Quadratic Surd

Cite this as:

Weisstein, Eric W. "Quadratic Surd." From MathWorld--A Wolfram Web Resource.

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