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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, a political party
• 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^{citation needed}
• Radical Baroque, in architecture

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