The Collaborative International Dictionary of English v.0.48:

Radically \Rad"i*cal*ly\ (r[a^]d"[i^]*kal*l[y^]), adv.
   1. In a radical manner; at, or from, the origin or root;
      fundamentally; as, a scheme or system radically wrong or
      defective.
      [1913 Webster]

   2. Without derivation; primitively; essentially. [R.]
      [1913 Webster]

            These great orbs thus radically bright. --Prior.
      [1913 Webster]

WordNet (r) 3.0 (2006):

radically
    adv 1: in a radical manner; "she took a radically different
           approach"