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In the case in which the cubic has only one real root, the real root is given by this expression with the radicands of the cube roots being real and with the cube roots being the real cube roots.
According to Cardano's formula, one of its roots (all of them, actually) can be expressed as the sum of a cube root of + with a cube root of . On ...
By analogy with the cube root of x, ... Equivalently, if the real tetrahedral root n of x is an integer, x is the n th tetrahedral number. Properties
The space diagonal of the unit cube is √ 3. Distances between vertices of a double unit cube are square roots of the first six natural numbers, including the square root of 3 (√7 is not possible due to Legendre's three-square theorem) This projection of the Bilinski dodecahedron is a rhombus with diagonal ratio √ 3.
The twelfth root of two or (or equivalently /) is an algebraic irrational number, approximately equal to 1.0594631. It is most important in Western music theory , where it represents the frequency ratio ( musical interval ) of a semitone ( Play ⓘ ) in twelve-tone equal temperament .
real root of x 3 = x + 1: ... The algebraic solution of a reduced quintic equation can be written in terms of square roots, cube roots and the Bring radical.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
The Debye–Hückel theory was proposed by Peter Debye and Erich Hückel as a theoretical explanation for departures from ideality in solutions of electrolytes and plasmas. It is a linearized Poisson–Boltzmann model, which assumes an extremely simplified model of electrolyte solution but nevertheless gave accurate predictions of mean activity coefficients for ions in dilute solution.