'nonrationally' originates from English, specifically formed from the prefix 'non-' + the adjective 'rational' + the adverbial suffix '-ly'. 'Rational' ultimately originates from Latin, specifically the word 'rationalis', where 'ratio' meant 'reason'.

'rational' changed from Latin 'rationalis' through Old French 'rationel' into Middle English 'rational'; the productive English prefix 'non-' was added to form 'nonrational', and the suffix '-ly' then formed 'nonrationally'.

Initially, Latin 'rationalis' meant 'relating to reason'; over time, with the addition of the negating prefix 'non-' and adverbial suffix '-ly', the modern term came to mean 'in a manner not governed by reason'.