irrational number

noun

Any real number that cannot be expressed as a ratio of two integers.

“The square root of a positive integer is an irrational number unless the positive integer is a perfect square, in which case the square root will also be a positive integer.”

Similar
irrational
Opposite
rational number
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Meanings

nounirrational number (plural irrational numbers)

plural irrational numbers

  1. mathematicsAny real number that cannot be expressed as a ratio of two integers.

    The square root of a positive integer is an irrational number unless the positive integer is a perfect square, in which case the square root will also be a positive integer.

Synonyms & antonyms

Opposite
rational number

nouna real number that cannot be expressed as a rational number

Similar
irrational
Broader
real numberreal
Also see
irrational

Synonym sets from Open English WordNet, CC BY 4.0.

Translations

Bulgarian ирациона́лно число́
  • ирациона́лно число́ (iracionálno čisló)real number that is not rational
Catalan nombre irracional
  • nombre irracionalreal number that is not rational
Chinese Mandarin 無理數 /无理数
  • 無理數 /无理数 (wúlǐshù)real number that is not rational
Czech iracionální číslo
  • iracionální čísloreal number that is not rational
Esperanto neracionala nombro
  • neracionala nombroreal number that is not rational
Finnish irrationaaliluku
  • irrationaalilukureal number that is not rational
French nombre irrationnel
  • nombre irrationnelreal number that is not rational
German irrationale Zahl
  • irrationale Zahlreal number that is not rational
Greek άρρητος αριθμός
  • άρρητος αριθμός (árritos arithmós)real number that is not rational
Hindi अपरिमेय संख्या
  • अपरिमेय संख्या (aprimey saṅkhyā)real number that is not rational
Hungarian irracionális szám
  • irracionális számreal number that is not rational
Icelandic óræð tala
  • óræð talareal number that is not rational
Indonesian bilangan irasional
  • bilangan irasionalreal number that is not rational
Irish uimhir éagóimheasta
  • uimhir éagóimheastareal number that is not rational
Italian numero irrazionale
  • numero irrazionalereal number that is not rational
Japanese 無理数
  • 無理数 (murisū)real number that is not rational
Korean 무리수
  • 무리수 (murisu)real number that is not rational
Latin numerus irrationalis
  • numerus irrationalisreal number that is not rational
Māori tau kewha
  • tau kewhareal number that is not rational
Polish liczba niewymierna
  • liczba niewymiernareal number that is not rational
Portuguese número irracional
  • número irracionalreal number that is not rational
Romanian număr irațional
  • număr iraționalreal number that is not rational
Russian иррациона́льное число́
  • иррациона́льное число́ (irracionálʹnoje čisló)real number that is not rational
Spanish número irracional
  • número irracionalreal number that is not rational
Tagalog bilang na ditagwayin
  • bilang na ditagwayinreal number that is not rational
Thai จำนวนอตรรกยะ
  • จำนวนอตรรกยะ (jam-nuuan-à-dtàk-gà-yá)real number that is not rational
Turkish irrasyonel sayı
  • irrasyonel sayıreal number that is not rational
Vietnamese số vô tỉ
  • số vô tỉreal number that is not rational
Cite this entry
APA

irrational number. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/irrational%20number

MLA

“irrational number.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/irrational%20number. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “irrational number,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/irrational%20number.

Source: irrational number on Wiktionary, CC BY-SA 4.0.