'approvably' originates from English formation of the adjective 'approvable' (from the verb 'approve') with the adverbial suffix '-ly'. 'approve' ultimately comes from Latin 'approbare', where 'ad-' meant 'to' and 'probare' meant 'to test, prove'.

'approve' entered English via Old French (aprovier/aprouver) from Latin 'approbare'; later the adjective 'approvable' was formed in English by adding the suffix '-able', and 'approvably' was formed by adding '-ly' to that adjective.

Initially related to the action 'to approve' (to show assent or confirm); over time the derived adjective and adverb came to mean 'capable of being approved' and 'in a way that can be approved', respectively.