nonrational

adjective
non·ra·tio·nal | \ ˌnän-ˈrash-nəl , -ˈra-shə-nᵊl \

Definition of nonrational 

1 : not based on, guided by, or employing reason : not rational : irrational nonrational beliefs nonrational behavior … anthropological history exploring such nonrational aspects of society as mating customs and eating habits. —Gertrude Himmelfarb

2 mathematics : not relating to or being a rational number : irrational nonrational numbers

First Known Use of nonrational

1859, in the meaning defined above

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The first known use of nonrational was in 1859

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