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Cube root. In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other ...
A root of degree 2 is called a square root (usually written without the n as just ) and a root of degree 3, a cube root (written ). 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 .
A cube number, or a perfect cube, or sometimes just a cube, is a number which is the cube of an integer . The non-negative perfect cubes up to 60 3 are (sequence A000578 in the OEIS ):
The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions ). All of the roots of the cubic equation can be found by the following means:
Imaginary numbers are an important mathematical concept; they extend the real number system to the complex number system in which at least one root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra ). Here, the term "imaginary" is used because there is no real number having a negative square .
Here the function is f(x) = (x3 + 3x2 − 6x − 8)/4. In mathematics, a cubic function is a function of the form that is, a polynomial function of degree three. In many texts, the coefficients a, b, c, and d are supposed to be real numbers, and the function is considered as a real function that maps real numbers to real numbers or as a complex ...
A cubic field is called a pure cubic field if it can be obtained by adjoining the real cube root of a cube-free positive integer n to the rational number field Q. Such fields are always complex cubic fields since each positive number has two complex non-real cube roots.
Radical symbol. In mathematics, the radical symbol, radical sign, root symbol, radix, or surd is a symbol for the square root or higher-order root of a number. The square root of a number x is written as. while the n th root of x is written as. It is also used for other meanings in more advanced mathematics, such as the radical of an ideal .
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