'approvability' is formed in Modern English by adding the noun-forming suffix '-ity' to the adjective 'approvable', which in turn derives from the verb 'approve'.

'approve' entered Middle English from Old French 'aprover' (or 'aprover') and ultimately from Latin 'approbare' (from ad- 'to' + probare 'to test, prove'); the adjective 'approvable' developed in later English, and 'approvability' is a modern nominal derivative.

The Latin root 'probare' originally meant 'to test, try, prove'; over time the sense shifted through Old French and Middle English to mean 'to assent to, declare fit', and modern 'approvability' now denotes the potential to be approved rather than the act of testing.