root out vs exterminate

root out and exterminate both are verbs.

Word	Noun	Adjective	Verb	Adverb
root out	No	No	Yes	No
exterminate	No	No	Yes	No

As verbs, root out and exterminate are synonyms defined as:

Other synonyms of root out include eradicate, extirpate, uproot.

root out (verb)	exterminate (verb)
pull up by or as if by the roots	kill en masse; kill on a large scale; kill many
destroy completely, as if down to the roots	destroy completely, as if down to the roots