'unapprovableness' originates from English, formed by the negative prefix 'un-' (Old English) added to the adjective 'approvable', which ultimately comes from Latin 'approbare' (from 'ad-' + 'probare'), where 'ad-' meant 'toward' and 'probare' meant 'to test, prove, approve'.

'approve' came into English via Old French 'aprover' from Latin 'approbare'; from this developed the adjective 'approvable' in English, and by adding the prefix 'un-' and the nominalizing suffix '-ness' the modern noun 'unapprovableness' was formed.

Initially the root sense concerned 'proving' or 'testing' (Latin 'probare'); over time the derivative 'approvable' came to mean 'able to be approved', and 'unapprovableness' now denotes 'the quality of not being able to be approved' or 'unacceptability'.