irrational

UK: /ɪˈræʃ^ənəl/ US: /ɪˈræʃənəl/ ,(i rash′ə nl)

WordReference Random House Learner's Dictionary of American English © 2025

ir•ra•tion•al /ɪˈræʃənəl/   adj. 

1. lacking sound judgment or logic:
   an irrational argument.
2. not controlled or governed by reason:
   irrational behavior.
3. not having the power of reason:
   Brute animals are irrational beings.
4. Mathematics (of a number) that cannot be expressed exactly as a ratio of two integers:
   The value of pi is an irrational number.

ir•ra•tion•al•ly, adv. See -ratio-.

WordReference Random House Unabridged Dictionary of American English © 2025

ir•ra•tion•al  (i rash′ə nl), adj. 

1. without the faculty of reason;
   deprived of reason.
2. without or deprived of normal mental clarity or sound judgment.
3. not in accordance with reason;
   utterly illogical:
   irrational arguments.
4. not endowed with the faculty of reason:
   irrational animals.
5. [Math.]
   • Mathematics (of a number) not capable of being expressed exactly as a ratio of two integers.
   • Mathematics (of a function) not capable of being expressed exactly as a ratio of two polynomials.
6. Mathematics [Algebra.] (of an equation) having an unknown under a radical sign or, alternately, with a fractional exponent.
7. Poetry [Gk. and Lat. Pros.]
   • of or pertaining to a substitution in the normal metrical pattern, esp. a long syllable for a short one.
   • noting a foot or meter containing such a substitution.

n. 

8. [Math.] See irrational number. 

• Latin irratiōnālis. See ir-², rational
• late Middle English 1425–75

ir•ra′tion•al•ly, adv. 
ir•ra′tion•al•ness, n. 
Synonyms

• 3. unreasonable, ridiculous; insensate.

Collins Concise English Dictionary © HarperCollins Publishers::

irrational / ɪˈræʃən^əl/ adjective

1. inconsistent with reason or logic; illogical; absurd
2. incapable of reasoning
3. not rational
4. (as noun): an irrational

irˈrationally adverb