radical

Etymology

Inherited from Middle English radical, from Latin rādīcālis (“of or pertaining to the root, having roots, radical”).

adj

1. Favoring fundamental change, or change at the root cause of a matter.
   His beliefs are radical.
2. (botany, not comparable) Pertaining to a root (of a plant).
3. Pertaining to the basic or intrinsic nature of something.
4. Thoroughgoing; far-reaching.
   The spread of the cancer required radical surgery, and the entire organ was removed.
   Phoenix and Lubbock are both caught in severe drought, and it is going to get much worse. We may see many such [dust] storms in the decades ahead, along with species extinctions, radical disturbance of ecosystems, and intensified social conflict over land and water. Welcome to the Anthropocene, the epoch when humans have become a major geological and climatic force. 2012-01, Donald Worster, “A Drier and Hotter Future”, in American Scientist, volume 100, number 1, archived from the original on 2012-01-26, page 70
5. (lexicography, not comparable) Of or pertaining to the root of a word.
6. (phonology, phonetics, not comparable, of a sound) Produced using the root of the tongue.
7. (chemistry, not comparable) Involving free radicals.
8. (mathematics) Relating to a radix or mathematical root.
   a radical quantity; a radical sign
9. (slang, 1980s & 1990s) Excellent; awesome.
   That was a radical jump!

noun

1. (historical, 19th-century Britain) A member of the most progressive wing of the Liberal Party; someone favouring social reform (but generally stopping short of socialism).
2. (historical, early 20th-century France) A member of an influential, centrist political party favouring moderate social reform, a republican constitution, and secular politics.
3. A person with radical opinions.
4. (arithmetic) A root (of a number or quantity).
5. (linguistics) In logographic writing systems such as the Chinese writing system, the portion of a character (if any) that provides an indication of its meaning, as opposed to phonetic.
6. (linguistics) In Celtic languages, refers to the basic, underlying form of an initial consonant which can be further mutated under the Celtic initial consonant mutations.
7. (linguistics) In Semitic languages, any one of the set of consonants (typically three) that make up a root.
8. (chemistry) A group of atoms, joined by covalent bonds, that take part in reactions as a single unit.
9. (organic chemistry) A free radical.
10. (algebra, commutative algebra, ring theory, of an ideal) Given an ideal I in a commutative ring R, another ideal, denoted Rad(I) or √, such that an element x ∈ R is in Rad(I) if, for some positive integer n, xⁿ ∈ I; equivalently, the intersection of all prime ideals containing I.
11. (algebra, ring theory, of a ring) Given a ring R, an ideal containing elements of R that share a property considered, in some sense, "not good".
12. (algebra, ring theory, of a module) The intersection of maximal submodules of a given module.
13. (number theory) The product of the distinct prime factors of a given positive integer.