Meaning

• (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).

• (historical: early 20th-century France) A member of an influential, centrist political party favouring moderate social reform, a republican constitution, and secular politics.

• A person with radical opinions.

• A root (of a number or quantity).

• 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.

• In Semitic languages, any one of the set of consonants (typically three) that make up a root.

• A group of atoms, joined by covalent bonds, that take part in reactions as a single unit.

• A free radical.

• (commutative algebra, of an ideal) Given an ideal I in a commutative ring R, another ideal, denoted Rad(I) or \sqrt{I}, 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.

• (of a ring) Given a ring R, an ideal containing elements of R that share a property considered, in some sense, "not good".

• (of a module) The intersection of maximal submodules of a given module.

• The product of the distinct prime factors of a given positive integer.

Meaning

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

  "His beliefs are radical."

• Pertaining to a root (of a plant).

• Pertaining to the basic or intrinsic nature of something.

• Thoroughgoing; far-reaching.

  "The spread of the cancer required radical surgery, and the entire organ was removed."

• Of or pertaining to the root of a word.

• (of a sound) Produced using the root of the tongue.

• Involving free radicals.

• Relating to a radix or mathematical root.

  "a radical quantity; a radical sign"

• (1980s & 1990s) Excellent; awesome.

  "That was a radical jump!"