Merriam-Webster's Collegiate® Dictionary, 11th Edition
IRRATIONAL
I. adjective
Etymology: Middle English, from Latin irrationalis, from in- + rationalis rational
Date: 14th century
not rational: as, a. not endowed with reason or understanding, lacking usual or normal mental clarity or coherence, not governed by or according to reason , c. Greek & Latin prosody having a quantity other than that required by the meter, containing such a syllable, d. being an irrational number , having a numerical value that is an irrational number , irrationality noun irrationally adverb
II. noun
Date: 1646
an irrational being, irrational number