LATIN DICTIONARYLexicon Latīnum
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“irrational” in Latin

The English word irrational itself goes back to Latin ratiō, through irratiōnālis.

Riddle & Arnold A Copious and Critical English–Latin Lexicon, 1864

irrational
rationis expers (not gifted with reason): brutus (without the faculty or capacity of perception): mutus (mute, unreasonable, inasmuch as speech implies reason; all three of animals): demens (senseless, and also of things that none but a senseless person would do): insanus (mad, deprived of right reason, insane; of men; then also denoting excess; e.g., moles, montes). An irrational animal or being, bestia (opposed to homo). In an irrational manner; Vid: IRRATIONALLY.

Quick answer

What is the Latin word for irrational?
The usual Latin words for “irrational” are brūtus, mūtus, dēmō; also īnsānus, mōlēs, bēstia. The right choice depends on the sense; see the distinctions below.

Entry from J. E. Riddle & T. K. Arnold, A Copious and Critical English–Latin Lexicon (rev. C. Anthon, New York: Harper, 1864), digitised by Fergus J. P. Walsh, CC BY-SA 4.0; Latin markup adapted by latindictionary.co.