Radical

**Radical**, from Late Latin *radicalis* "of roots" and from Latin *radix* "root", may refer to:

;in science and mathematics
*A radical (chemistry) is an atom, molecule, or ion which is likely to take part in chemical reactions.
*Radical symbol (√), a symbol used to indicate the square root or nth root
*Radical of an algebraic group, a concept in algebraic group theory
*Radical of an ideal, an important concept in abstract algebra
*Radical of a ring, in ring theory, a branch of mathematics, a radical of a ring is an ideal of "bad" elements of the ring
*Radical of a module, in the theory of modules, the radical of a module is a component in the theory of structure and classification
*Jacobson radical, the Jacobson radical of a ring, R, consists of those elements in R which annihilate all simple right R-modules
*Nilradical of a ring, the nilradical of a commutative ring is a nilpotent ideal, which is as large as possible
*Nilradical of a Lie algebra, the nilradical of a lie algebra is a nilpotent ideal, which is as large as possible
*Radical of an integer, a concept in number theory
*Symmetric bilinear form, a concept in linear algebra
*Radical of a Lie algebra, a concept in lie theory

;in medicine
*Radical surgery, surgery carried out in extreme circumstances and/or with extensive treatment

;in linguistics
*Root (linguistics), also called a "radical", the form of a word after any prefixes and suffixes are removed
*Radical (Chinese character), part of a Chinese character under which it is indexed in a dictionary (also called bùshǒu 部首)
*Radical, one of the three consonants in a Semitic root
*Radical consonant, a consonant articulated with the root of the tongue

;in politics
*Political radicalism
**Radicalism (historical), the Radical Movement which began in late 18th century Britain and spread to continental Europe and Latin America in the 19th century
**Radical left, another term for the far left
**Radical right, another term for the far right
**radical - a person who shows a strong political stand point
Extremism, political standpoints that are perceived as revolutionary or extreme
*Radical Whigs, influential early writers on Radicalism
*Radical Reformation, an Anabaptist movement at the time of the Protestant Reformation
*Radical Republicans, a member of an influential group of American politicians during the Civil War reconstruction
*Radical Party, one of a number of political parties around the world
*Radicals (UK), parliamentary progressives who were part of the nineteenth-century Liberal coalition
*Radical feminism, a current within feminism that focuses on patriarchy as a system of power
*Radical veganism, a radical interpretation of veganism, usually combined with anarchism

;in culture
*Radical chic, a term coined by Tom Wolfe to describe the pretentious adoption of radical causes by celebrities, socialites, and high society

;in architecture
*Radical Baroque, an architectural style characterized by the curvature of walls and intersection of oval spaces

;brands, titles and proper names
*Radical Sportscars, an English sports car maker
*Radical Entertainment, a video game developer based in Vancouver, Canada
*Free Radical Design, a video game developer based in Nottingham, England 
*Free Radicals (band), a jazz-funk musical group from Houston, Texas
*Free Radical Centre, a centre for free radical chemistry and biotechnology that was established in 2005
**Radical* (Smack album), Smack's fourth studio album, released in 1988