The Collaborative International Dictionary of English v.0.48:

Inextirpable \In`ex*tir"pa*ble\, a. [L. inexstirpabilis: cf. F.
   inextirpable. See In- not, and Extirpate.]
   Not capable of being extirpated or rooted out; ineradicable.
   [1913 Webster]

WordNet (r) 3.0 (2006):

inextirpable
    adj 1: incapable of extermination or extirpation; "some weeds
           seem inextirpable" [syn: inexterminable,
           inextirpable]