'ascertainableness' is formed in modern English by adding the suffix '-ness' to the adjective 'ascertainable' (itself 'ascertain' + '-able'). 'Ascertain' ultimately relates to Latin roots meaning 'certain'.

'ascertain' entered English via Old French (e.g. 'acerter'/'acertener'), from Latin-related roots tied to 'certus' ('certain'); with the adjectival suffix '-able' (meaning 'able to be') this produced 'ascertainable', and the noun-forming suffix '-ness' produced 'ascertainableness' in later English usage.

Initially related to making something 'certain' or 'sure', the formation came to mean the quality of being able to be determined or verified; the basic sense of 'can be made certain' has been retained.