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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.
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. For the definition of the principal square root of other complex numbers, see Square root § Principal square root of a complex number.
√ (radical symbol) 1. Denotes square root and is read as the square root of. For example, +. 2. With an integer greater than 2 as a left superscript, denotes an n th root. For example, denotes the 7th root of 3. ^ 1. Exponentiation is normally denoted with a superscript.
The radical symbol (√), for square root was introduced by Christoph Rudolff in the early 1500s.Michael Stifel's important work Arithmetica integra [54] contained important innovations in mathematical notation. In 1556, Niccolò Tartaglia used parentheses for precedence grouping.
radical symbol (for square root) 1637 (with the vinculum above the radicand) René Descartes (La Géométrie) % percent sign: 1650 (approx.) unknown
greek beta symbol u+03d1: ϑ: greek theta symbol u+03d2: ϒ: greek upsilon with hook symbol u+03d5: ϕ: greek phi symbol u+03f0: ϰ: greek kappa symbol u+03f1: ϱ: greek rho symbol u+03f4: ϴ: greek capital theta symbol u+03f5: ϵ: greek lunate epsilon symbol u+03f6 ϶ greek reversed lunate epsilon symbol
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.
U+2113 ℓ SCRIPT SMALL L; "despite its character name, this symbol is derived from a special italicized version of the small letter l". [6] It has various other specialized uses, such as a liter symbol and as the azimuthal quantum number symbol. U+2118 ℘ SCRIPT CAPITAL P is a symbol for Weierstrass's elliptic function. [7]