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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 of ...
In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 23 = 8 or (x + 1)3 . The cube is also the number multiplied by its square : n3 = n × n2 = n × n × n.
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 .
In mathematics, exponentiation is an operation involving two numbers: the base and the exponent or power.Exponentiation is written as b n, where b is the base and n is the power; this is pronounced as "b (raised) to the (power of) n ".
For a standard 27 ft (8.2 m) yacht: the cube root of 27 is 3, 3 squared is 9 plus 1 = 10. The beam of many 27 ft monohulls is 10 ft (3.05 m). For a Volvo Open 70 yacht: 70.5 to the power of 2/3 = 17 plus 1 = 18. The beam is often around 18 ft (5.5 m). For a 741 ft (226 m) long ship: the cube root is 9, and 9 squared is 81, plus 1.
The square–cube law was first mentioned in Two New Sciences (1638). The square–cube law (or cube–square law) is a mathematical principle, applied in a variety of scientific fields, which describes the relationship between the volume and the surface area as a shape's size increases or decreases. It was first [dubious – discuss] described ...
Definition. If K is a field extension of the rational numbers Q of degree [ K: Q ] = 3, then K is called a cubic field. Any such field is isomorphic to a field of the form. where f is an irreducible cubic polynomial with coefficients in Q. If f has three real roots, then K is called a totally real cubic field and it is an example of a totally ...
The definition then of an nth root of a number x is a number r (the root) which, when raised to the power of the positive integer n, yields x: r n = x . {\displaystyle r^{n}=x.} A root of degree 2 is called a square root (usually written without the n as just x {\displaystyle {\sqrt {x}}} ) and a root of degree 3, a cube root (written x 3 ...