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. 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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