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Cube root. 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 ...
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 .
Fast inverse square root, sometimes referred to as Fast InvSqrt () or by the hexadecimal constant 0x5F3759DF, is an algorithm that estimates , the reciprocal (or multiplicative inverse) of the square root of a 32-bit floating-point number in IEEE 754 floating-point format. The algorithm is best known for its implementation in 1999 in Quake III ...
An illustration of an unsolved Rubik's Cube. The Rubik's Cube is a 3D combination puzzle invented in 1974 [2] [3] by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, [4] the puzzle was licensed by Rubik to be sold by Pentangle Puzzles in the UK in 1978, [5] and then by Ideal Toy Corp in 1980 [6 ...
Doubling the cube is the construction, using only a straightedge and compass, of the edge of a cube that has twice the volume of a cube with a given edge. This is impossible because the cube root of 2, though algebraic, cannot be computed from integers by addition, subtraction, multiplication, division, and taking square roots.
Find the cube root of 456533. The cube root ends in 7. After the last three digits are taken away, 456 remains. 456 is greater than all the cubes up to 7 cubed. The first digit of the cube root is 7. The cube root of 456533 is 77. This process can be extended to find cube roots that are 3 digits long, by using arithmetic modulo 11.
Doubling the cube, also known as the Delian problem, is an ancient [a] [1] : 9 geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first. As with the related problems of squaring the circle and trisecting the angle, doubling the cube is now known to ...
Here the function is f(x) = (x3 + 3x2 − 6x − 8)/4. In mathematics, a cubic function is a function of the form that is, a polynomial function of degree three. In many texts, the coefficients a, b, c, and d are supposed to be real numbers, and the function is considered as a real function that maps real numbers to real numbers or as a complex ...