verb
exterminate implies the complete, wholesale destruction of things or living beings whose existence is considered undesirable; extirpate and eradicate both suggest the extinction or abolition of something, extirpate implying destruction at the very source, often through the loss or removal of conditions necessary for survival, and eradicate connoting less violence and, often, the working of natural processes or a methodical plan
See exterminate in Webster's New World Roget's A-Z Thesaurus II
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