ineradicable has no recorded synonym. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is eradicable.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
not able to be destroyed or rooted out
“ineradicable superstitions”
Synonyms, antonyms and the broader and narrower relations for ineradicable come from Princeton University’s WordNet. Full sources and licences.