root out has 5 distinct synonyms spread across 2 of its 2 senses. 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. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
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.
pull up by or as if by the roots
“uproot the vine that has spread all over the garden”
destroy completely, as if down to the roots
“the vestiges of political democracy were soon uprooted”
Synonyms, antonyms and the broader and narrower relations for root out come from Princeton University’s WordNet. Full sources and licences.