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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**.The

**cube root**law is an observation in political science that the number of members of a unicameral legislature, or the lower house of a bicameral legislature, is about the**cube root**of the population being represented. [1] The rule was devised by Rein Taagepera in his 1972 paper "The size of national assemblies". [2]The introductory paragraph begins: "In mathematics, the

**cube root**of a number, denoted or x 1/3, is the number a such that a3 = x. All real numbers have exactly one real**cube root**and 2 complex**roots**, and all nonzero complex numbers have 3 distinct complex**cube****roots**."File:

**Cube root**.svg. Size of this PNG preview of this SVG file: 460 × 244 pixels. Other resolutions: 320 × 170 pixels | 640 × 339 pixels | 1,024 × 543 pixels | 1,280 × 679 pixels | 2,560 × 1,358 pixels. This is a file from the Wikimedia Commons. Information from its description page there is shown below.The

**cube**function is the function x ↦ x3 (often denoted y = x3) that maps a number to its**cube**. It is an odd function, as (−n)3 = − (n3). The volume of a geometric**cube**is the**cube**of its side length, giving rise to the name. The inverse operation that consists of finding a number whose**cube**is n is called extracting the**cube root**of n.the cubic has three distinct real

**roots**If the cubic has one real**root**and two non-real complex conjugate**roots**. This can be proved as follows. First, if r is a**root**of a polynomial with real coefficients, then its complex conjugate is also a**root**. So the non-real**roots**, if any, occur as pairs of complex conjugate**roots**.Adjoining the real

**cube root**of 2 to the rational numbers gives the cubic field. Q ( 2 3 ) {\displaystyle \mathbf {Q} ( {\sqrt [ {3}] {2}})} . This is an example of a pure cubic field, and hence of a complex cubic field. In fact, of all pure cubic fields, it has the smallest discriminant (in absolute value ), namely −108.

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