radical

adj

1. Favoring fundamental change, or change at the root cause of a matter.

   “His beliefs are radical.”

2. (not-comparable)Pertaining to a root (of a plant).
3. Pertaining to the basic or intrinsic nature of something.

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

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.”

5. (not-comparable)Of or pertaining to the root of a word.
6. (not-comparable)Produced using the root of the tongue.
7. (not-comparable)Involving free radicals.
8. Relating to a radix or mathematical root.

   “a radical quantity; a radical sign”

9. (slang)Excellent; awesome.

   “That was a radical jump!”

noun

1. (historical)A member of the most progressive wing of the Liberal Party; someone favouring social reform (but generally stopping short of socialism).
2. (historical)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. A root (of a number or quantity).
5. In logographic writing systems such as the Chinese writing system, the portion of a character used to index it. Often, but not always, this is also the portion indicating meaning; compare the following sense.
6. (common, proscribed)In logographic writing systems such as the Chinese writing system, the portion of a character used to index it. Often, but not always, this is also the portion indicating meaning; compare the following sense.

   “The boy recognised the Chinese characters, though the calligraphy looked a bit strange, as if drawn by someone who had seen them and copied them out radical by radical without knowing what they meant.”

7. In Celtic languages, the basic, underlying form of an initial consonant which can be further mutated under the Celtic initial consonant mutations.
8. In Semitic languages, any one of the set of consonants (typically three) that make up a root.
9. A group of atoms, joined by covalent bonds, that take part in reactions as a single unit.
10. A free radical.
11. 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.
12. Given a ring R, an ideal containing elements of R that share a property considered, in some sense, "not good".
13. The intersection of maximal submodules of a given module.
14. The product of the distinct prime factors of a given positive integer.