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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**. For example, the real**cube root**of 8, denoted , is 2, because 23 = 8, while the other**cube****roots**...The other

**roots**of the equation are obtained either by changing of**cube root**or, equivalently, by multiplying the**cube root**by a primitive**cube root**of unity, that is . This formula for the**roots**is always correct except when p = q = 0 , with the proviso that if p = 0 , the**square****root**is chosen so that C ≠ 0 .Abū Kāmil Shujā ibn Aslam (Egypt, 10th century) in particular was the first to accept irrational numbers (often in the form of a

**square****root**,**cube root**or fourth**root**) as solutions to quadratic equations or as coefficients in an equation. The 9th century Indian mathematician Sridhara wrote down rules for solving quadratic equations.In algebraic terms, doubling a unit

**cube**requires the construction of a line segment of length x, where x 3 = 2; in other words, x = , the**cube root**of two. This is because a**cube**of side length 1 has a volume of 1 3 = 1, and a**cube**of twice that volume (a volume of 2) has a side length of the**cube root**of 2. The impossibility of doubling the ...In mathematics, an nth

**root**of a number x is a number r which, when raised to the power n, yields x : where n is a positive integer, sometimes called the degree of the**root**. 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 ...**Roots**of unity can be defined in any field. If the characteristic of the field is zero, the**roots**are complex numbers that are also algebraic integers. For fields with a positive characteristic, the**roots**belong to a finite field, and, conversely, every nonzero element of a finite field is a**root**of unity.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. The rule was devised by Estonian political scientist Rein Taagepera in his 1972 paper "The size of national assemblies".