'unapprovability' originates from English, specifically formed from the negative prefix 'un-' + adjective 'approvable' (from Latin 'approbare'), where the Latin prefix 'ad-' (appearing as 'ap-' before 'p') meant 'to' and 'probare' meant 'to test, prove, or approve'.

'approve' entered English via Old French/Anglo-Norman (Old French 'aprover') from Latin 'approbare'; the adjective 'approvable' and the negative prefix 'un-' combined in English to form 'unapprovable', and adding the noun-forming suffix '-ity' produced 'unapprovability'.

Initially the Latin root meant 'to test or prove'; in later usage this shifted toward the sense 'to agree with or give formal acceptance', and 'unapprovability' developed to mean 'the quality of not being acceptable or capable of being approved'.