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Nested radical. In algebra, a nested radical is a radical expression (one containing a square root sign, cube root sign, etc.) that contains (nests) another radical expression. Examples include. which arises in discussing the regular pentagon, and more complicated ones such as.
n. th root. In mathematics, an nth root of a number x is a number r (the root) which, when raised to the power of the positive integer n, yields x: The 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.
Rationalisation (mathematics) In elementary algebra, root rationalisation (or rationalization) is a process by which radicals in the denominator of an algebraic fraction are eliminated. If the denominator is a monomial in some radical, say with k < n, rationalisation consists of multiplying the numerator and the denominator by and replacing by ...
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the ...
A solution in radicals or algebraic solution is a closed-form expression, and more specifically a closed-form algebraic expression, that is the solution of a polynomial equation, and relies only on addition, subtraction, multiplication, division, raising to integer powers, and the extraction of n th roots (square roots, cube roots, and other integer roots).
An n×n matrix with n distinct nonzero eigenvalues has 2 n square roots. Such a matrix, A, has an eigendecomposition VDV−1 where V is the matrix whose columns are eigenvectors of A and D is the diagonal matrix whose diagonal elements are the corresponding n eigenvalues λi. Thus the square roots of A are given by VD1/2 V−1, where D1/2 is ...