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In number theory, the radical of a positive integer n is defined as the product of the distinct prime numbers dividing n. Each prime factor of n occurs exactly once as a factor of this product: r a d ( n ) = ∏ p ∣ n p prime p {\displaystyle \displaystyle \mathrm {rad} (n)=\prod _{\scriptstyle p\mid n \atop p{\text{ prime}}}p}
An unresolved root, especially one using the radical symbol, is sometimes referred to as a surd [2] or a radical. [3] Any expression containing a radical, whether it is a square root, a cube root, or a higher root, is called a radical expression , and if it contains no transcendental functions or transcendental numbers it is called an algebraic ...
In mathematics, the radical symbol, radical sign, root symbol, or surd is a symbol for the square root or higher-order root of a number.
In mathematics, a square root of a number x is a number y such that = ... The radicand is the number or expression underneath the radical sign, in this case, 9.
Radical expression involving roots, also known as an nth root Solution in radicals; Radical symbol (√), used to indicate the square root and other roots; 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, an ideal of "bad" elements of a ring
In 1637 Descartes was the first to unite the German radical sign √ with the vinculum to create the radical symbol in common use today. [8] The symbol used to indicate a vinculum need not be a line segment (overline or underline); sometimes braces can be used (pointing either up or down). [9]
A radical ideal (or semiprime ideal) is an ideal that is equal to its radical. The radical of a primary ideal is a prime ideal . This concept is generalized to non-commutative rings in the semiprime ring article.
has no real number solution since no real number squared equals −1. Sometimes a quadratic equation has a root of multiplicity 2, such as: (+) = For this equation, −1 is a root of multiplicity 2. This means −1 appears twice, since the equation can be rewritten in factored form as