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In number theory, the radical of a positive integer n is defined as the product of the distinct prime numbers dividing n. Each prime factor of n occurs exactly once as a factor of this product: r a d ( n ) = ∏ p ∣ n p prime p {\displaystyle \displaystyle \mathrm {rad} (n)=\prod _{\scriptstyle p\mid n \atop p{\text{ prime}}}p}
The hydroxyl radical, Lewis structure shown, contains one unpaired electron. Lewis dot structure of a Hydroxide ion compared to a hydroxyl radical. In chemistry, a radical, also known as a free radical, is an atom, molecule, or ion that has at least one unpaired valence electron.
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 ...
Notation for the (principal) square root of x. For example, √ 25 = 5, since 25 = 5 ⋅ 5, or 5 2 (5 squared). In mathematics, a square root of a number x is a number y such that =; in other words, a number y whose square (the result of multiplying the number by itself, or ) is x. [1]
Methylene spontaneously autopolymerises to form various excited oligomers, the simplest of which, is the excited form of the alkene ethylene. The excited oligomers, decompose rather than decay to a ground state. For example, the excited form of ethylene decomposes to acetylene and atomic hydrogen. [10] 2 CH 2 → H 2 CCH * 2 → HCCH + 2 H
His formula is again mentioned by Eutokios in a commentary on Archimedes. [4] In 499 CE Aryabhata, a mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy, gave a method for finding the cube root of numbers having many digits in the Aryabhatiya (section 2.5). [5]
The chemical formula can be written R−C· or R−C 3· (also written as ⫶C−R), or just CH. Carbynes can be seen as derivatives of the simplest such compound, the methylidyne radical or unsubstituted carbyne H−C· or H−C 3· , in which the functional group is a hydrogen atom.
The radical symbol refers to the principal value of the square root function called the principal square root, which is the positive one. The two square roots of a negative number are both imaginary numbers , and the square root symbol refers to the principal square root, the one with a positive imaginary part.