word-forming element meaning "away," from Latin a "off, of, away from," the usual form of Latin ab before consonants (see ab-). As in avert, avocation. It is also the a in a priori and the à in Thomas à Kempis, Thomas à Becket.
late 14c., racional, "pertaining to or springing from reason;" mid-15c., of persons, "endowed with reason, having the power of reasoning," from Old French racionel and directly from Latin rationalis "of or belonging to reason, reasonable," from ratio (genitive rationis) "reckoning, calculation, reason" (see ratio).
In arithmetic, "expressible in finite terms," 1560s. Meaning "conformable to the precepts of practical reason" is from 1630s. Related: Rationally. It is from the same source as ratio and ration; the sense in rational is aligned with that in related reason (n.), which got deformed in French.
<a href="https://www.etymonline.com/word/arational">Etymology of arational by etymonline</a>
Harper, D. (n.d.). Etymology of arational. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/arational