Lewis & Short

irrătĭōnālis (inr-), e, adj. [2. in-rationalis], without reason, irrational (postAug.): animal, Quint. 7, 3, 3; 24; Sen. Ep. 113, 17; 118, 14; 124, 23: usus, mechanical exercises, Quint. 10, 7, 11: anima, Tert. Poen. 12.
Subst.: irrătĭōnālĭa, ĭum, n. plur., things or creatures without reason: de irrationalibus, Quint. 8, 6, 13.
Adv.: irră-tĭōnālĭter, irrationally, Tert. adv. Marc. 2, 6 al.