'approximable' originates from Latin, specifically the verb 'approximare' (past participle 'approximatus'), where the prefix 'ad-' (appearing as 'ap-') meant 'to' or 'toward' and 'proximus' meant 'near'.

'approximare' passed into Medieval Latin and influenced Old French and Middle English forms (such as 'aproximat'/'approximate'), and the English adjective was formed by combining the root with the adjectival suffix '-able' to create 'approximable'.

Initially related to 'making near' or 'bringing close' (literally 'to make near'), it evolved to the modern sense of 'able to be approximated or estimated' in scientific and general usage.