The Collaborative International Dictionary of English v.0.48:

Radical \Rad"i*cal\ (r[a^]d"[i^]*kal), a. [F., fr. L. radicalis
   having roots, fr. radix, -icis, a root. See Radix.]
   1. Of or pertaining to the root; proceeding directly from the
      root.
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   2. Hence: Of or pertaining to the root or origin; reaching to
      the center, to the foundation, to the ultimate sources, to
      the principles, or the like; original; fundamental;
      thorough-going; unsparing; extreme; as, radical evils;
      radical reform; a radical party.
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            The most determined exertions of that authority,
            against them, only showed their radical
            independence.                         --Burke.
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   3. (Bot.)
      (a) Belonging to, or proceeding from, the root of a plant;
          as, radical tubers or hairs.
      (b) Proceeding from a rootlike stem, or one which does not
          rise above the ground; as, the radical leaves of the
          dandelion and the sidesaddle flower.
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   4. (Philol.) Relating, or belonging, to the root, or ultimate
      source of derivation; as, a radical verbal form.
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   5. (Math.) Of or pertaining to a radix or root; as, a radical
      quantity; a radical sign. See below.
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   Radical axis of two circles. (Geom.) See under Axis.

   Radical pitch, the pitch or tone with which the utterance
      of a syllable begins. --Rush.

   Radical quantity (Alg.), a quantity to which the radical
      sign is prefixed; specifically, a quantity which is not a
      perfect power of the degree indicated by the radical sign;
      a surd.

   Radical sign (Math.), the sign [root] (originally the
      letter r, the initial of radix, root), placed before any
      quantity, denoting that its root is to be extracted; thus,
      [root]a, or [root](a + b). To indicate any other than the
      square root, a corresponding figure is placed over the
      sign; thus, [cuberoot]a, indicates the third or cube root
      of a.

   Radical stress (Elocution), force of utterance falling on
      the initial part of a syllable or sound.

   Radical vessels (Anat.), minute vessels which originate in
      the substance of the tissues.
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   Syn: Primitive; original; natural; underived; fundamental;
        entire.

   Usage: Radical, Entire. These words are frequently
          employed as interchangeable in describing some marked
          alteration in the condition of things. There is,
          however, an obvious difference between them. A radical
          cure, reform, etc., is one which goes to the root of
          the thing in question; and it is entire, in the sense
          that, by affecting the root, it affects in an
          appropriate degree the entire body nourished by the
          root; but it may not be entire in the sense of making
          a change complete in its nature, as well as in its
          extent. Hence, we speak of a radical change; a radical
          improvement; radical differences of opinion; while an
          entire change, an entire improvement, an entire
          difference of opinion, might indicate more than was
          actually intended. A certain change may be both
          radical and entire, in every sense.
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WordNet (r) 3.0 (2006):

radical sign
    n 1: a sign indicating the extraction of a root