Word
irrational
Phoneticsir·ra·tional
US/ˌɪˈɹæʃənəɫ/
UK/ɪɹˈæʃənəl/
Definitions
01not logical
B2 · Upper Intermediate
adj. not based on reason or clear thinking.
adj. lacking logical justification or sound reasoning; often used to describe emotions, fears, or decisions.
“She had an irrational fear of spiders, even though she knew they were harmless.”
“The market's reaction was entirely irrational, driven more by panic and hearsay than by any concrete changes in economic data.”
Synonyms
Antonyms
02mathematical numbers
C1 · Advanced Mathematics Technical
adj. describes a number that cannot be written as a simple fraction.
adj. relating to a real number that cannot be expressed as a ratio of two integers.
“Pi is the most famous example of an irrational number.”
“The proof that the square root of two is irrational remains a fundamental exercise in introductory number theory.”
Antonyms
03an irrational number
C1 · Advanced Countable noun Mathematics Technical
n. a number that cannot be made by dividing two whole numbers.
n. a real number that cannot be expressed as a quotient of two integers.
“In this math problem, you need to identify which of these values are irrationals.”
“The set of real numbers is composed of both rationals and irrationals, though the latter are far more numerous.”
Synonyms
Antonyms
Real-World Examples
“When we are convinced that someone is wrong, we may conclude that they are biased or irrational .” Etymology
From Latin irratiōnālis, from ir- + ratiōnālis.
Etymology adapted from Wiktionary, available under CC BY-SA 4.0.
Word family
NOUN
ADJECTIVE
ADVERB
Domain
- Exam level
- CambridgeCambridgeCambridge English QualificationsThe exam suite from Cambridge University Press & Assessment, from A1 Movers up to C2 Proficiency. The benchmark names double as CEFR labels.B2 FirstIELTSIELTSInternational English Language Testing SystemThe 0–9 band test co-owned by the British Council, IDP, and Cambridge. Used for university entry, work, and migration.5.5–6.5TOEFL iBTTOEFL iBTTest of English as a Foreign Language, Internet-Based TestETS's academic English test, the standard route for US university admissions. Scored 0–120, with a 1–6 scale since 2026.1–6 scale: 4.0–4.572–94TOEICTOEICTest of English for International CommunicationETS's workplace English test, big in Japan and Korea. Listening & Reading scores 10–990 and tops out at C1.785–944
- Frequency
- Frequent
- Level
- B2 · Upper Intermediate
- Updated
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