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inextirpable (adj.)

1620s, from in- (1) "not, opposite of" + extirpable (see extirpate).

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Definitions of inextirpable from WordNet

inextirpable (adj.)
incapable of extermination or extirpation;
some weeds seem inextirpable
Synonyms: inexterminable
From wordnet.princeton.edu