Eradicate, v. t. [imp. & p. p. Eradicated; p. pr. & vb. n. Eradicating.]
Etymology: [L. eradicatus, p. p. of eradicare to eradicate; e out + radix, radicis, root. See Radical.]
1. To pluck up by the roots; to root up; as, an oak tree eradicated.
2. To root out; to destroy utterly; to extirpate; as, to eradicate diseases, or errors. This, although now an old an inveterate evil, might be eradicated by vigorous treatment. Southey.
Syn. -- To extirpate; root out; exterminate; destroy; annihilate.
Shades of meaning
Fernald has no entry of its own for eradicate; he lists it under abolish, exterminate.
Where he writes about it:
Eradicate (L. e, out, and radix, root) is primarily applied to numbers or groups of plants which it is desired to remove effectually from the soil; a single tree may be uprooted, but is not said to be eradicated; we labor to eradicate or root out noxious weeds. — from exterminate
To extirpate (L. ex, out, and stirps, stem, stock) is not only to destroy the individuals of any race of plants or animals, but the very stock, so that the race can never be restored; we speak of eradicating a disease, of extirpating a cancer, exterminating wild beasts or hostile tribes; we seek to eradicate or extirpate all vices and evils. — from exterminate