radical, in chemistry, group of atoms that are joined together in some particular spatial structure and that take part in most chemical reactions as a single unit. Important inorganic radicals include ammonium, NH₄; carbonate, CO₃ ; chlorate, ClO₃, and perchlorate, ClO₄ ; cyanide, CN; hydroxide, OH; nitrate, NO₃; phosphate, PO₄; silicate, SiO₃ (meta) or SiO₄ (ortho); and sulfate, SO₄. The use of these radicals simplifies the naming and description of inorganic compounds, since such usage does not consider the electronic charge on the group. (When ions are dealt with, electronic charge must be considered.) In organic chemistry, the term radical is sometimes used synonymously with group; e.g., the group CH₃ is sometimes called the methyl radical instead of the methyl group. This use is limited chiefly to alkyl groups and aryl groups; it is usually not applied to functional groups, such as carbonyl. Because the term radical easily could be taken to mean a free radical, the term group is preferred by some.

radical, in mathematics, symbol placed over a number or expression, called the radicand, to indicate a root of the radicand. When used without a sign or index number, it designates the positive square root of the radicand, i.e., 2. If both square roots are meant, the radical sign is preceded by ±. To indicate higher roots of the radicand, e.g., cube or fourth roots, an index number is used. The radical sign is generally taken to indicate the principal root of the radicand, although any radicand will have n different nth roots. The term radical is sometimes used loosely to refer to the entire expression consisting of radical sign and radicand.

Term used in chemistry with one predominant and two subsidiary, looser meanings. It most often refers to a free radical. It can also mean an ion or a functional group.

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Radical (from Latin radicis, genitive of radix "root") can refer to many different things and concepts.

Mathematics

• The 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 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

Chemistry

• Radical (chemistry) or free radical, atomic or molecular species with unpaired electrons

Linguistics

• Radical consonant, which involves the root of the tongue
• Radical (Chinese character), part of a Chinese character under which it is indexed in a dictionary (also called bùshǒu 部首)
• One of the three consonants in a Semitic trilateral or quadrilateral root

Society

• 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
• Extremism, political standpoints that are perceived as revolutionary or extreme

• Radical Whigs, influential early writers on Radicalism
• Radical Republican (USA), 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
• Industrial Radicals, members of the fictional Industrial Radical Party
• Religious radicalism

Businesses and organizations

• 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, TX
• Radical Matters, a record label
• Free Radical Centre

Music albums

• Radical (Smack album), Smack's fourth studio album, released in 1988

Other

• In cabinet making, another way of saying external plinth
• Radical Baroque, in architecture