The most determined exertions of that authority, against them, only showed their radical independence. Burke.

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 ***radic] (originally the letter r, the initial of radix, root), placed before any quantity, denoting that its root is to be extracted; thus, ***radic]a, or ***radic](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.

Syn. -- Primitive; original; natural; underived; fundamental; entire. -- 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.

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.

As a general rule, the metallic atoms are basic radicals, while the nonmetallic atoms are acid radicals. J. P. Cooke.

(b)

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.)