In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other cube roots of 8 are and . The three cube roots of −27i are:
In some contexts, particularly when the number whose cube root is to be taken is a real number, one of the cube roots (in this particular case the real one) is referred to as the principal cube root, denoted with the radical sign The cube root is the inverse function of the cube function if considering only real numbers, but not if considering also complex numbers: although one has always the cube of a nonzero number has more than one complex cube root and its principal cube root may not be the number that was cubed. For example, , but
Plot of y = 3√x. The plot is symmetric with respect to origin, as it is an odd function. At x = 0 this graph has a vertical tangent.A unit cube (side = 1) and a cube with twice the volume (side = 3√2 = 1.2599... OEIS: A002580).
because a cube of side length 1 has a volume of 13 = 1, and a cube of twice that volume (a volume of 2) has a side length of the cuberoot of 2. The impossibility...
first that require cube roots. There are 6 primitive seventh roots of unity, which are pairwise complex conjugate. The sum of a root and its conjugate...
The cuberoot law is an observation in political science that the number of members of a unicameral legislature, or of the lower house of a bicameral...
number x of which the root is taken is the radicand. A root of degree 2 is called a square root and a root of degree 3, a cuberoot. Roots of higher degree...
the cuberoot of it must end in 1. If the perfect cube ends in 2, the cuberoot of it must end in 8. If the perfect cube ends in 3, the cuberoot of it...
Wantzel proved it to be impossible because the cuberoot of 2 is not a constructible number. The cube has three uniform colorings, named by the unique...
symbol, radical sign, root symbol, radix, or surd is a symbol for the square root or higher-order root of a number. The square root of a number x is written...
by 6 is a simple algorithmic calculation. Extracting the square root or the cuberoot of a number using mathematical models is a more complex algorithmic...
nested radical is a radical expression (one containing a square root sign, cuberoot sign, etc.) that contains (nests) another radical expression. Examples...
demonstrated an approximate trisection of angles and implied construction of a cuberoot was impossible. In 1922, Harry Houdini published "Houdini's Paper Magic...
is a cuberoot of unity, 1 + 3 + 3 2 ≡ 13 ( mod 26 ) {\displaystyle 1+3+3^{2}\equiv 13{\pmod {26}}} meaning that it is not a principal cuberoot of unity...
number field Q and p(x) = x3 − 2. Each root of p equals 3√2 times a cuberoot of unity. Therefore, if we denote the cube roots of unity by ω 1 = 1 , {\displaystyle...
={\frac {-1+i{\sqrt {3}}}{2}}=e^{i2\pi /3}} is a primitive (hence non-real) cuberoot of unity. The Eisenstein integers form a triangular lattice in the complex...
root of their product, that is, 2 ⋅ 8 = 4 {\displaystyle {\sqrt {2\cdot 8}}=4} . The geometric mean of the three numbers 4, 1, and 1/32 is the cube root...
arithmetic operations as far as taking the square root, although he explains how to find the cube and cube-root of an integer and later gives rules facilitating...
{\displaystyle K=\mathbb {Q} (\theta ,\omega )} where θ is a cuberoot of 2, and ω is a cuberoot of 1 (but not 1 itself). If we consider K inside the complex...
especially for the cuberoot. The Binomial Cube The trinomial cube is similar to the binomial cube, but has the following pieces instead: 1 red cube and 6 black...
out to be quite correct; scientists eventually converged on a roughly cube-root curve, consistent with the Stevens's power law for brightness perception...
between 0 and 1. The geometric mean of the three indices—that is, the cuberoot of the product of the indices—is the human development index. A value...
_{4}(q)^{4}]} The formulas for the theta Nullwert function values from the cuberoot of the elliptic nome are obtained by contrasting the two real solutions...
The CubeRoot of Uncertainty is a collection of science fiction short stories by American writer Robert Silverberg, published in hardcover by Macmillan...
square root of 2 is constructible. However, the cuberoot of 2 is not constructible; this is related to the impossibility of doubling the cube. A real...
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