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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.
A root (also known as a root word or radical) is the core of a word that is irreducible into more meaningful elements. [1] In morphology , a root is a morphologically simple unit which can be left bare or to which a prefix or a suffix can attach.
The square root of a positive integer is the product of the roots of its prime factors, because the square root of a product is the product of the square roots of the factors. Since p 2 k = p k , {\textstyle {\sqrt {p^{2k}}}=p^{k},} only roots of those primes having an odd power in the factorization are necessary.
Radical expression involving roots, also known as an nth root; Radical symbol (√), used to indicate the square root and other roots; Radical of an algebraic group, a concept in algebraic group theory; Radical of an ideal, an important concept in abstract algebra; Radical of a ring, an ideal of "bad" elements of a ring
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 ...
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 ...
The radical of an ideal in a commutative ring, denoted by or , is defined as = { +}, (note that ).Intuitively, is obtained by taking all roots of elements of within the ring.
A radical was then identified as the root base of certain acids (the Latin word "radix" meaning "root"). Historically, the term radical in radical theory was also used for bound parts of the molecule, especially when they remain unchanged in reactions.