Webster's Revised Unabridged Dictionary · 1913

Radical

Radical (rad"i*kal) , adjective

[French, from Latin radicalis having roots, from radix, -icis, a root. See Radix.]

1.
Of or pertaining to the root; proceeding directly from the root.
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.
The most determined exertions of that authority, against them, only showed their radical independence. — Burke
3.
(a) (Botany) Belonging to, or proceeding from, the root of a plant; as, radical tubers or hairs.
(b)
(Botany) 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.
4.
(Philology) Relating, or belonging, to the root, or ultimate source of derivation; as, a radical verbal form.
5.
(Mathematics) Of or pertaining to a radix or root; as, a radical quantity; a radical sign. See below.
Collocations (6)
Radical axis of two circles (Geometry) , See under Axis.
Radical pitch , the pitch or tone with which the utterance of a syllable begins. — Rush
Radical quantity (Algebra) , 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 (Mathematics) , the sign r (originally the letter r, the initial of radix, root), placed before any quantity, denoting that its root is to be extracted; thus, ra, or r(a + b). To indicate any other than the square root, a corresponding figure is placed over the sign; thus, ca, 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 (Anatomy) , minute vessels which originate in the substance of the tissues.

Radical (rad"i*kal) , noun

1.
(a) (Philology) A primitive word; a radix, root, or simple, underived, uncompounded word; an etymon.
(b)
(Philology) A primitive letter; a letter that belongs to the radix.
The words we at present make use of, and understand only by common agreement, assume a new air and life in the understanding, when you trace them to their radicals, where you find every word strongly stamped with nature; full of energy, meaning, character, painting, and poetry. — Cleland
2.
(Politics) One who advocates radical changes in government or social institutions, especially such changes as are intended to level class inequalities; -- opposed to conservative.
In politics they [the Independents] were, to use the phrase of their own time, “Root-and-Branch men,” or, to use the kindred phrase of our own, Radicals. — Macaulay
3.
(a) (Chemistry) A characteristic, essential, and fundamental constituent of any compound; hence, sometimes, an atom.
As a general rule, the metallic atoms are basic radicals, while the nonmetallic atoms are acid radicals. — J. P. Cooke
(b)
Specifically, a group of two or more atoms, not completely saturated, which are so linked that their union implies certain properties, and are conveniently regarded as playing the part of a single atom; a residue; -- called also a compound radical. Compare Residue.
4.
(Algebra) A radical quantity. See under Radical, a.
An indicated root of a perfect power of the degree indicated is not a radical but a rational quantity under a radical form. — Davies & Peck (Math. Dict.)
5.
(Anatomy) A radical vessel. See under Radical, a.