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 concurrent with 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