'nonrational' originates from English, specifically the prefix 'non-' (from Latin 'non' meaning 'not') joined with 'rational' which originates from Latin 'rationalis', where 'ratio' meant 'reason'.

'rational' changed from Late Latin word 'rationalis' (from Latin 'ratio') into Middle English via Old French and eventually became the modern English word 'rational'; the negative prefix 'non-' (from Latin 'non', adopted into Old/Middle English) was attached to form 'nonrational'.

Initially it meant 'not endowed with reason' or simply 'not rational'; over time the term has been used both in ordinary language to mean 'irrational/unreasonable' and in mathematics to denote numbers not expressible as a ratio of integers ('irrational' numbers).