'unapprovable' originates from a combination: the prefix 'un-' from Old English 'un-' meaning 'not' and 'approvable' ultimately from Latin 'approbare', where 'ad-' meant 'to' and 'probare' meant 'to test/approve'.

'approve' came into English via Old French 'aprover' and Middle English forms (e.g. 'aprouven'); 'approvable' developed as an adjective from 'approve', and the productive negative prefix 'un-' was attached to form 'unapprovable' in modern English.

Originally the root 'probare' carried the sense 'to test or prove' and evolved into the sense 'to give formal approval'; 'unapprovable' therefore came to mean 'not able to be approved' or 'not deserving approval'.