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QuadraticIrrationalQ[x]

gives True if x is a quadratic irrational and False otherwise.

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Basic Examples  
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QuadraticIrrationalQ

QuadraticIrrationalQ[x]

gives True if x is a quadratic irrational and False otherwise.

Details

  • QuadraticIrrationalQ[x] tests whether x can be expressed in the form , where , and are integers.
  • Quadratic irrationals have continued fractions that are ultimately periodic.

Examples

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Basic Examples  (1)

Scope  (4)

Rational numbers are not quadratic irrationals:

is a transcendental number:

QuadraticIrrationalQ threads element-wise over lists:

QuadraticIrrationalQ returns False if not given an explicit quadratic irrational:

Wolfram Research (2007), QuadraticIrrationalQ, Wolfram Language function, https://reference.wolfram.com/language/ref/QuadraticIrrationalQ.html.

Text

Wolfram Research (2007), QuadraticIrrationalQ, Wolfram Language function, https://reference.wolfram.com/language/ref/QuadraticIrrationalQ.html.

CMS

Wolfram Language. 2007. "QuadraticIrrationalQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/QuadraticIrrationalQ.html.

APA

Wolfram Language. (2007). QuadraticIrrationalQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/QuadraticIrrationalQ.html

BibTeX

@misc{reference.wolfram_2025_quadraticirrationalq, author="Wolfram Research", title="{QuadraticIrrationalQ}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/QuadraticIrrationalQ.html}", note=[Accessed: 28-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_quadraticirrationalq, organization={Wolfram Research}, title={QuadraticIrrationalQ}, year={2007}, url={https://reference.wolfram.com/language/ref/QuadraticIrrationalQ.html}, note=[Accessed: 28-August-2025]}