The words rational (adjective) and rationale (noun) may look and even sound a bit alike, but their meanings are quite different.
Rational has almost the same meaning as logical. In fact, rational and logical are interchangeable. However, logical implies the rules of logic, while rational can simply mean wise:
Mary always made rational choices, never taking any foolish risks, or wasting money. (wise)
Rational thought should be independent of emotions. (logical)
A rationale, in contrast, is a reason that justifies an action or decision (a justification)—usually a purpose:
Cody’s rationale for changing homes was to save money.