'unapproximable' originates from Modern English, specifically formed from the prefix 'un-' + the adjective 'approximable', where 'un-' meant 'not' and 'approximable' ultimately traces to Latin 'approximare' meaning 'to come near'.

'approximable' changed from Middle English 'approximate' (from Old French/Anglo-Norman forms) and ultimately from Late Latin 'approximatus' / the verb 'approximare', and eventually became the modern English adjective 'approximable', from which 'unapproximable' was formed.

Initially the root meant 'to come near' or 'to bring near' (Latin sense); over time it developed the adjectival sense 'able to be approximated' and the modern negated form means 'not able to be approximated'.