radical

(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.

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!”