Phrase guide

irrational number

noun · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

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

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, sciences

Examples

  • 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.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

a real number that cannot be expressed as a rational number

Definition source: Princeton WordNet 3.0

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: irrational

Antonyms: none provided

Broader terms: real number, real

Narrower terms: transcendental number, algebraic number

History

Etymology

No etymology was provided for this word.

Across languages

Translations

32 source translations are retained for this English entry.

  • Armenian: իռացիոնալ թիվ (iṙacʻional tʻiv) — real number that is not rational
  • Bulgarian: ирациона́лно число́ (iracionálno čisló) — real number that is not rational
  • Catalan: nombre irracional — real number that is not rational
  • Chinese Mandarin: 無理數 /无理数 (wúlǐshù) — real number that is not rational
  • Czech: iracionální číslo — real number that is not rational
  • Esperanto: neracionala nombro — real number that is not rational
  • Finnish: irrationaaliluku — real number that is not rational
  • French: nombre irrationnel — real number that is not rational
  • German: irrationale Zahl — real number that is not rational
  • Greek: άρρητος αριθμός (árritos arithmós) — real number that is not rational
  • Hindi: अपरिमेय संख्या (aprimey saṅkhyā) — real number that is not rational
  • Hungarian: irracionális szám — real number that is not rational
  • Icelandic: óræð tala — real number that is not rational
  • Indonesian: bilangan irasional — real number that is not rational
  • Irish: uimhir éagóimheasta — real number that is not rational
  • Italian: numero irrazionale — real number that is not rational
  • Japanese: 無理数 (murisū) — real number that is not rational
  • Kazakh: иррационал сан (irrasional san) — real number that is not rational
  • Korean: 무리수 (murisu) — real number that is not rational
  • Latin: numerus irrationalis — real number that is not rational
  • Macedonian: ирациона́лен број (iracionálen broj) — real number that is not rational
  • Māori: tau kewha — real number that is not rational
  • Polish: liczba niewymierna — real number that is not rational
  • Portuguese: número irracional — real number that is not rational
  • Romanian: număr irațional — real number that is not rational
  • Russian: иррациона́льное число́ (irracionálʹnoje čisló) — real number that is not rational
  • Serbo-Croatian: ирaционaлни брой — real number that is not rational
  • Serbo-Croatian: iracionalni broj — real number that is not rational
  • Spanish: número irracional — real number that is not rational
  • Tagalog: bilang na ditagwayin — real number that is not rational
  • Turkish: irrasyonel sayı — real number that is not rational
  • Vietnamese: số vô tỉ — real number that is not rational