Webster’s 1913 has no entry under this spelling.
Shades of meaning
Fernald has no entry of its own for root out; he lists it under 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