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• in sociology:
  • one who advocates thoroughgoing analysis or change "at the root"
• in politics:
  • can refer to (an extremist) a supporter of a revolutionary social movement
  • can refer to a counterpart to a conservative; see Radical Republican
  • can refer to member of a Radical Party
  • can refer to a progressive liberal, like e.g. the Radicals, a group of left-wing MPs in the 19th-century British Parliament
• in chemistry, either an atom or molecule with at least one unpaired electron, or a group of atoms, charged or uncharged, that act as a single entity in reaction. These two definitions are not functionally identical. (see radical (chemistry)The term radical can have two distinct meanings in chemistry. The first is that a radical is an atom or molecule with free unpaired electrons. This causes them to be highly reactive as they try to bond these electrons with other atoms. In this sense, a ra).
• in mathematicsMathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of "figures and numbers". In the formalist view, it is the investigation of axiomatically defined abstract structures:
  • the n-th radical or rootIn mathematics, a root (or a zero of a function f is an element x in the domain of f such that f ''x 0. Consider the equation. Now 3 is called a root of f because f 3) 0. If the function is mapping from real numbers to real numbers, its zeros are essentia of a number a, written as , which is a number whose n-th power is a (see radical (mathematics)See radical for other uses of the term In mathematics, the n th root or radical of the non-negative real number a written as , is the unique non-negative real number b such that b n ''a''. See square root for the case where n 2. Fundamental operations Ope).
  • the radical of an algebraic groupIn mathematics, an algebraic group G contains a unique maximal normal solvable subgroup; and this subgroup is closed. Its identity component is called the radical of G''. Algebraic groups Group theory. is a concept in algebraic groupIn algebraic geometry, two important classes of algebraic group arise, that for the most part are studied separately. The general definition of algebraic group is the expected one: a group in the category of algebraic varieties; or, more simply, a group w theory.
  • the radical of an idealIn ring theory, a branch of mathematics, the radical of a ring isolates certain bad properties of the ring. There are several different kinds of radicals, such as the nilradical and the Jacobson radical as well as a theory of general radical properties. is an important concept in abstract algebraAbstract algebra Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. The term "abstract algebra" is used to distinguish the field from " elementary algebra" or "high school algebr.
• in linguistics, a part of a Chinese character (see radical (Chinese character)).