for some positive integer n. For example, 2 is a root of 16 since 24 = 2 × 2 × 2 × 2 = 16.
The number n is called the degree of the root. A root of degree 2 is called a square root, a root of degree 3 is called a cube root, a root of degree 4 is called a fourth root, and so forth. In general, a root of degree n is called an nth root. Roots are usually written using the radical symbol , with denoting the square root, denoting the cube root, denoting the fourth root, and so on.
In calculus, roots are treated as special cases of exponentiation, where the exponent is a fraction:
- .
Roots are particularly important in the theory of infinite series, where the root test determines the radius of convergence of a power series. Roots can also be defined for complex numbers, and the complex roots of 1 (the roots of unity) play an important role in higher mathematics. Much of Galois theory is concerned with determining which algebraic numbers can be expressed using roots, leading to the famous Abel-Ruffini theorem that a general polynomial of degree five or higher cannot be solved using roots alone.
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unknown
ue, 15 Apr 2008 15:26:31 GM
Addition +; Subtraction -; Multiplication *; Division /; exponentiation (to the power of) ^; modulo (remainder after division) %; . root. exponentiation (. root. of . nth. number) 5th . root. of 32; Factorial ! And much more! ...
