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radical, in mathematics, symbol (art/radical.gif) placed over a number or expression, called the radicand, to indicate a root of the radicand. When used without a sign or index number, as in 4art/square-root-of-4.gif, it designates the positive square root of the radicand, i.e., 2. If both square roots are meant, the radical sign is preceded by ±, as in ±4art/square-root-of-4.gif. To indicate higher roots of the radicand, e.g., cube or fourth roots, an index number is used, as in 327art/cube-root-of-27.gif. The radical sign is generally taken to indicate the principal root of the radicand, i.e., 327art/cube-root-of-27.gif = 3, although any radicand will have n different n th roots. The term radical is sometimes used loosely to refer to the entire expression consisting of radical sign and radicand.

The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

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