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A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
A solution in radicals or algebraic solution is an expression of a solution of a polynomial equation that is algebraic, that is, relies only on addition, subtraction, multiplication, division, raising to integer powers, and extraction of n th roots (square roots, cube roots, etc.). A well-known example is the quadratic formula
In mathematics, a sum of radicals is defined as a finite linear combination of n th roots: =, where , are natural numbers and , are real numbers.. A particular special case arising in computational complexity theory is the square-root sum problem, asking whether it is possible to determine the sign of a sum of square roots, with integer coefficients, in polynomial time.
In numerical analysis, the Runge–Kutta methods (English: / ˈ r ʊ ŋ ə ˈ k ʊ t ɑː / ⓘ RUUNG-ə-KUUT-tah [1]) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous nonlinear equations. [2]
SRS can be solved in polynomial time in the Real RAM model. [3] However, its run-time complexity in the Turing machine model is open, as of 1997. [1] The main difficulty is that, in order to solve the problem, the square-roots should be computed to a high accuracy, which may require a large number of bits.
In the case of two nested square roots, the following theorem completely solves the problem of denesting. [2]If a and c are rational numbers and c is not the square of a rational number, there are two rational numbers x and y such that + = if and only if is the square of a rational number d.
A matrix B is said to be a square root of A if the matrix product BB is equal to A. [1] Some authors use the name square root or the notation A 1/2 only for the specific case when A is positive semidefinite, to denote the unique matrix B that is positive semidefinite and such that BB = B T B = A (for real-valued matrices, where B T is the ...
In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form + + to the form + for some values of and . [1] In terms of a new quantity x − h {\displaystyle x-h} , this expression is a quadratic polynomial with no linear term.
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