Irrational square number

In mathematics, a is square irrational number (also square irrational number , engl. Quadratic surds ) an irrational algebraic number , which are the solution of a quadratic equation with rational coefficients is obtained. Based on the formula solution to the quadratic equation one can see that each square irrational number in the form of three integers , , can be displayed. There is no square number. Fixed and variable and result in elements of a square number field . ${\displaystyle {a\pm {\sqrt {b}} \over c}}$ ${\displaystyle a}$ ${\displaystyle b>0}$ ${\displaystyle c\neq 0}$ ${\displaystyle b}$ ${\displaystyle b}$ ${\displaystyle a}$ ${\displaystyle c}$

Squared irrational numbers are particularly interesting in relation to continued fractions because they, and only they, have periodic continued fraction expansions.

Example:

${\displaystyle {\sqrt {3}}=1{,}73205\ldots =[1;1,2,1,2,1,2,\ldots ]=[1;{\overline {1,2}}]}$