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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
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011.
Radical elimination can be viewed as the reverse of radical addition. In radical elimination, an unstable radical compound breaks down into a spin-paired molecule and a new radical compound. Shown below is an example of a radical elimination reaction, where a benzoyloxy radical breaks down into a phenyl radical and a carbon dioxide molecule. [7]
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 ...
Radical extensions occur naturally when solving polynomial equations in radicals. In fact a solution in radicals is the expression of the solution as an element of a radical series: a polynomial f over a field K is said to be solvable by radicals if there is a splitting field of f over K contained in a radical extension of K.
Radical disproportionation encompasses a group of reactions in organic chemistry in which two radicals react to form two different non-radical products. Radicals in chemistry are defined as reactive atoms or molecules that contain an unpaired electron or electrons in an open shell. The unpaired electrons can cause radicals to be unstable and ...
In the third type of substitution reaction, radical substitution, the attacking particle is a radical. [44] This process usually takes the form of a chain reaction, for example in the reaction of alkanes with halogens. In the first step, light or heat disintegrates the halogen-containing molecules producing radicals.
A trivalent group 14 radical (also known as a trivalent tetrel radical) is a molecule that contains a group 14 element (E = C, Si, Ge, Sn, Pb) with three bonds and a free radical, having the general formula of R 3 E•. Such compounds can be categorized into three different types, depending on the structure (or equivalently the orbital in which ...