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Each positive real number has two square roots, one positive and the other negative. The radical symbol refers to the principal value of the square root function called the principal square root, which is the positive one.
The radicand is the number or expression underneath the radical sign, in this case, 9. For non-negative x , the principal square root can also be written in exponent notation, as x 1 / 2 {\displaystyle x^{1/2}} .
The function is multiplicative (but not completely multiplicative).. The radical of any integer is the largest square-free divisor of and so also described as the square-free kernel of . [2]
The positive integer n is called the index or degree, and the number x of which the root is taken is the radicand. A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred by using ordinal numbers, as in fourth root, twentieth root, etc. The computation of an n th root is a root extraction.
Radical expression involving roots, also known as an nth root; Radical symbol (√), used to indicate the square root and other roots; Radical of an algebraic group, a concept in algebraic group theory
This page was last edited on 4 December 2013, at 19:11 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
In the following, the quantity + is the whole radicand, and thus has a vinculum over it: a b + 2 n . {\displaystyle {\sqrt[{n}]{ab+2}}.} In 1637 Descartes was the first to unite the German radical sign √ with the vinculum to create the radical symbol in common use today.
In the case of three real roots, the square root expression is an imaginary number; here any real root is expressed by defining the first cube root to be any specific complex cube root of the complex radicand, and by defining the second cube root to be the complex conjugate of the first one.