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Cube root calculator reduces any number to simplest radical form; Computing the Cube Root, Ken Turkowski, Apple Technical Report #KT-32, 1998. Includes C source code. Weisstein, Eric W. "Cube Root". MathWorld
This free software had an earlier incarnation, Macsyma. Developed by Massachusetts Institute of Technology in the 1960s, it was maintained by William Schelter from 1982 to 2001. In 1998, Schelter obtained permission to release Maxima as open-source software under the GNU General Public license and the source code was released later that year ...
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
Free modified BSD license: Python-based TI-Nspire CAS (Computer Software) Texas Instruments: 2006 2009 5.1.3: 2020 Proprietary: Successor to Derive. Based on Derive's engine used in TI-89/Voyage 200 and TI-Nspire handheld Wolfram Alpha: Wolfram Research: 2009 2013: Pro version: $4.99 / month, Pro version for students: $2.99 / month, ioRegular ...
Here is an angle in the unit circle; taking 1 / 3 of that angle corresponds to taking a cube root of a complex number; adding −k 2 π / 3 for k = 1, 2 finds the other cube roots; and multiplying the cosines of these resulting angles by corrects for scale.
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.
An unresolved root, especially one using the radical symbol, is sometimes referred to as a surd [2] or a radical. [3] Any expression containing a radical, whether it is a square root, a cube root, or a higher root, is called a radical expression , and if it contains no transcendental functions or transcendental numbers it is called an algebraic ...
The simple Durand–Kerner and the slightly more complicated Aberth method simultaneously find all of the roots using only simple complex number arithmetic. Accelerated algorithms for multi-point evaluation and interpolation similar to the fast Fourier transform can help speed them up for large degrees of the polynomial. It is advisable to ...