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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.
radical symbol (for square root) 1637 (with the vinculum above the radicand) ... 1801 (first appearance in print; used previously in personal writings of Gauss)
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.
He introduced the radical symbol (√) for the square root. It is believed that this was because it resembled a lowercase "r" (for "radix"), [ 3 ] [ 4 ] though there is no direct evidence. [ 5 ] Cajori only says that a "dot is the embryo of our present symbol for the square root" [ 6 ] though it is "possible, perhaps probable" that Rudolff's ...
The radical symbol (√), for square root, was introduced by Christoph Rudolff in the early 1500s.Michael Stifel's important work Arithmetica integra [53] contained important innovations in mathematical notation. In 1556 Niccolò Tartaglia used parentheses for precedence grouping.
A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred by using ordinal numbers, as in fourth root, twentieth root, etc. The computation of an n th root is a root extraction. For example, 3 is a square root of 9, since 3 2 = 9, and −3 is also a square root of 9, since (−3) 2 = 9.
The square root of two is the frequency ratio of a tritone interval in twelve-tone equal temperament music. The square root of two forms the relationship of f-stops in photographic lenses, which in turn means that the ratio of areas between two successive apertures is 2.
√ (square-root symbol) Denotes square root and is read as the square root of. Rarely used in modern mathematics without a horizontal bar delimiting the width of its argument (see the next item). For example, √2. √ (radical symbol) 1. Denotes square root and is read as the square root of.