ineradicable adj.

word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."

In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.

early 15c., "destroy utterly," literally "pull up by the roots," from Latin eradicatus, past participle of eradicare "root out, extirpate, annihilate," from assimilated form of ex "out" (see ex-) + radix (genitive radicis) "root" (from PIE root *wrād- "branch, root"). Related: Eradicated; eradicating; eradicable. The native form of the same idea is in Middle English outrōten "to root (something) out, eradicate" (early 15c.).