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- Quadratic_irrational abstract "In mathematics, a quadratic irrational (also known as a quadratic irrationality or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients. Since fractions in the coefficients of a quadratic equation can be cleared by multiplying both sides by their common denominator, a quadratic irrational is an irrational root of some quadratic equation whose coefficients are integers. The quadratic irrationals form the real algebraic numbers of degree 2 and can, therefore, be expressed in this form:for integers a, b, c, d; with b and d non-zero, and with c > 1 and square-free. This implies that the quadratic irrationals have the same cardinality as ordered quadruples of integers, and are therefore countable.The rational numbers together with all quadratic irrationals with a given c form a field, called a real quadratic field. In particular, their inverses are of the same form, since This field is often called the field obtained by adjoining √c to the rational numbers, and denoted Q(√c). Quadratic irrationals have useful properties, especially in relation to continued fractions, where we have the result that all quadratic irrationals, and only quadratic irrationals, have periodic continued fraction forms. For example".
- Quadratic_irrational wikiPageExternalLink EIsIrrational.html.
- Quadratic_irrational wikiPageExternalLink surd.html.
- Quadratic_irrational wikiPageID "305331".
- Quadratic_irrational wikiPageRevisionID "589890824".
- Quadratic_irrational hasPhotoCollection Quadratic_irrational.
- Quadratic_irrational subject Category:Number_theory.
- Quadratic_irrational comment "In mathematics, a quadratic irrational (also known as a quadratic irrationality or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients. Since fractions in the coefficients of a quadratic equation can be cleared by multiplying both sides by their common denominator, a quadratic irrational is an irrational root of some quadratic equation whose coefficients are integers.".
- Quadratic_irrational label "Irracional quadrático".
- Quadratic_irrational label "Irrationnel quadratique".
- Quadratic_irrational label "Quadratic irrational".
- Quadratic_irrational label "Quadratisch irrationale Zahl".
- Quadratic_irrational label "عدد غير جذري تربيعي".
- Quadratic_irrational label "二次無理數".
- Quadratic_irrational sameAs Quadratisch_irrationale_Zahl.
- Quadratic_irrational sameAs Irrationnel_quadratique.
- Quadratic_irrational sameAs Irracional_quadrático.
- Quadratic_irrational sameAs m.01sfnh.
- Quadratic_irrational sameAs Q2006396.
- Quadratic_irrational sameAs Q2006396.
- Quadratic_irrational wasDerivedFrom Quadratic_irrational?oldid=589890824.
- Quadratic_irrational isPrimaryTopicOf Quadratic_irrational.