radical

from The American Heritage® Dictionary of the English Language, 5th Edition.

• adjective Arising from or going to a root or source; basic.
• adjective Departing markedly from the usual or customary; extreme or drastic.
• adjective Relating to or advocating fundamental or revolutionary changes in current practices, conditions, or institutions.
• adjective Medicine Relating to or being surgery that is extreme or drastic in an effort to eradicate all existing or potential disease.
• adjective Linguistics Of or being a root.
• adjective Of, relating to, or arising from a root.
• adjective Arising from the base of a stem or from a below-ground stem or rhizome.
• adjective Slang Excellent; wonderful.
• noun One who advocates fundamental or revolutionary changes in current practices, conditions, or institutions.
• noun Mathematics The root of a quantity as indicated by the radical sign.
• noun An atom or a group of atoms with one unpaired electron.
• noun Any of the basic Chinese characters that are combined to form more complex characters.
• noun Any of the traditional set of basic strokes or groups of strokes that make up Chinese characters and are used to classify and organize them in dictionaries.

from The Century Dictionary.

• Pertaining or relating to a root or to roots.
• Specifically— In botany, belonging to the root: opposed to cauline. See radical leaves and radical peduncle, below.
• In philology, of the nature of or pertaining to a root, or a primary or underived word or main part of a word: as, a radical word; a radical letter or syllable; radical accentuation.
• In mathematics, consisting of or indicating one of the roots of a number: as, a radical expression; the radical sign.
• In chem., noting any atom or group of atoms which is, for the moment, regarded as a chief constituent of the molecules of a given compound, and which does not lose its integrity in the ordinary chemical reactions to which the substance is liable.
• Making part of the essential nature of the subject or thing concerned; existing inherently; intrinsic; organic: as, radical defects of character; a radical fault of construction; the radical principles of an art or of religion.
• Of or pertaining to the root or foundation of the subject; concerned with or based upon fundamental principles; hence, thoroughgoing; extreme: as, a radical truth; a radical difference of opinion; radical views or measures; the Radical party in British politics.
• Of or pertaining to a political party or body of persons known as Radicals (see II., 4, below): as, a Radical candidate; the Radical program.
• Synonyms There may be a distinction between a radical reform, change, cure, or the like, and one that is thorough, entire, complete, or thoroughgoing, radical emphasizing only the fact of going to the root, whether there is thoroughness or entireness or not. Yet that which is radical is likely to be thorough, etc.
• noun In philology:
• noun A radical word or part of a word; especially, a primitive word or verbal element serving as a root of inflected or derivative words.
• noun A radical letter; a letter forming an essential part of the primitive form or root of a word. Also radicle.
• noun In chem., an element or group of combined elements which remains after one or more elements have been removed from a compound. (See the quotation.)
• noun In music, same as root.
• noun A person who holds or acts according to radical principles; one who pursues a theory to its furthest apparent limit; an extremist, especially in politics.
• noun In algebra, a quantity expressed as a root of another quantity.
• noun See the adjectives.
• In astrology, belonging to the radix or original scheme of nativity; in horary astrology, ripe and proper for judgment.
• noun A minute vessel which unites with others to form a large branch or trunk. See radicle, 2.
• noun In England, the name given to a white hat which was formerly somewhat worn by Radicals, owing to the fact that Henry Hunt [a radical English politician, 1773–1835] wore a white hat at various political gatherings in 1820.

from the GNU version of the Collaborative International Dictionary of English.

• adjective Of or pertaining to the root; proceeding directly from the root.
• adjective 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
• adjective Belonging to, or proceeding from, the root of a plant.
• adjective Proceeding from a rootlike stem, or one which does not rise above the ground.
• adjective (Philol.) Relating, or belonging, to the root, or ultimate source of derivation.
• adjective (Math.) Of or pertaining to a radix or root
• adjective (Geom.) See under Axis.
• adjective the pitch or tone with which the utterance of a syllable begins.
• adjective (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.
• adjective (Math.) the sign √ (originally the letter r, the initial of radix, root), placed before any quantity, denoting that its root is to be extracted; thus, √a, or √(a + b). To indicate any other than the square root, a corresponding figure is placed over the sign; thus, ∛a, indicates the third or cube root of a.
• adjective (Elocution) force of utterance falling on the initial part of a syllable or sound.
• adjective (Anat.) minute vessels which originate in the substance of the tissues.