5. (Math.)
Defn: Of or pertaining to a radix or root; as, a radical quantity; a radical sign. See below. 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 sq. root (originally the letter r, the initial of radix, root), placed before any quantity, denoting that its root is to be extracted; thus, sq. roota, or sq. root(a + b). To indicate any other than the square root, a corresponding figure is placed over the sign; thus cube roota, 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.
Syn. — Primitive; original; natural; underived; fundamental; entire. — Radical, Entire. These words are frequently employed as interchangeable in describing some marked alternation 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 a 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.
RADICAL
Rad"i*cal, n.
1. (Philol.) (a) A primitive word; a radix, root, or simple, underived, uncompounded word; an etymon. (b) 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)
Defn: 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 phrase of their own time. "Root-and-Branch men," or, to use the kindred phrase of our own, Radicals. Macaulay.
3. (Chem.) (a) 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. Cf. Residue.
4. (Alg.)
Defn: 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. )