Luckily, we don't have to rely on "O" when defining words, since we have an authoritative, citable source in the Oxford English Dictionary.
Radical
ADJECTIVE
Of or relating to a root or to roots.
1.a.
-
Of, belonging to, or from a root or roots; fundamental to or inherent in the natural processes of life, vital; spec. designating the humour or moisture once thought to be present in all living organisms as a necessary condition of their vitality; usually in radical heat, radical humidity, radical humour, radical moisture, radical sap*. Now historical.
1.b.
Of a quality, attribute, or feature: inherent in the nature or essence of a person or thing; fundamental. Now rare.
2.
Relating to or forming the root, basis, or foundation of something; original, primary.
3.a.
Mathematics. Originally: †(of a number) irrational (obsolete). In later use: relating to or forming the root of a number or quantity.
3.b.
Geometry. Having a common relation to two or more (esp. intersecting) circles or spheres. Chiefly in radical axis, centre, plane, etc.
4.a.
Linguistics. Of, belonging to, or relating to the root of a word; connected with or based on a root or roots; that is a root.
4.b.
1623–1765 Exhibiting the roots of words, or letters employed in those roots. Obsolete.
5.
1621–1819 Astrology and (occasionally) Astronomy. Belonging to the radix of an astrological or astronomical calculation; (of a question) asked at a time when the governing planet is also, or of the same triplicity as, a planet in the ascendant. Obsolete.
6.
Medicine and Surgery. Of a treatment: directed against the root or cause of disease, esp. towards the eradication of tumour or infection; curative, as opposed to palliative; spec. (of a surgical operation) involving extensive resection of tissue, esp. in order to remove a primary tumour and sites of actual or potential local spread and metastasis. Frequently in radical cure. Also in figurative context.
7.a.
Esp. of change or action: going to the root or origin; touching upon or affecting what is essential and fundamental; thorough, far-reaching.
7.b.
Politics. Advocating thorough or far-reaching political or social reform; representing or supporting an extreme section of a party; spec. (also with capital initial) (a) British belonging to, supporting, or associated with the group or movement which called for reform of the parliamentary system and other radical social and political changes in the late 18th and early 19th cent.; (b) U.S. belonging to a faction of the Republican Party seeking extreme action against the South during the Civil War and Reconstruction. Now more generally: revolutionary, esp. left-wing.
7.c.
Characterized by independence of or departure from what is usual or traditional; progressive, unorthodox, or innovative in outlook, conception, design, etc.
8.
Music. Of a bass, cadence, etc.: belonging to the root or lowest note of a chord.
9.
Botany. Of or relating to the root of a plant; esp. designating a basal leaf appearing to arise from the root (usually arising from the stem base or from a shortened stem).
10.
1836 - 1846. Anatomy. Of the nature of a radicle. Obsolete. rare.
11.
slang.(a) Originally Surfing challenging; extreme; (b) (more generally) excellent, fantastic.