Cube root in the context of Calculating

The sector, also known as a sector rule, proportional compass, or military compass, is a major calculating instrument that was in use from the end of the sixteenth century until the nineteenth century. It is an instrument consisting of two rulers of equal length joined by a hinge. A number of scales are inscribed upon the instrument which facilitate various mathematical calculations. It is used for solving problems in proportion, multiplication and division, geometry, and trigonometry, and for computing various mathematical functions, such as square roots and cube roots. Its several scales permitted easy and direct solutions of problems in gunnery, surveying and navigation. The sector derives its name from the fourth proposition of the sixth book of Euclid, where it is demonstrated that similar triangles have their like sides proportional. Some sectors also incorporated a quadrant, and sometimes a clamp at the end of one leg which allowed the device to be used as a gunner's quadrant.

A calculation is a deliberate mathematical process that transforms a plurality of inputs into a singular or plurality of outputs, known also as a result or results. The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm, to the vague heuristics of calculating a strategy in a competition, or calculating the chance of a successful relationship between two people.

For example, multiplying 7 by 6 is a simple algorithmic calculation. Extracting the square root or the cube root of a number using mathematical models is a more complex algorithmic calculation.

In mathematics, an nth root of a number x is a number r which, when raised to the power of n, yields x: $${\displaystyle r^{n}=\underbrace {r\times r\times \dotsb \times r} _{n{\text{ factors}}}=x.}$$ The positive integer n is called the index or degree, and the 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 cube root. Roots of higher degree are referred by using ordinal numbers, as in fourth root, twentieth root, etc. The computation of an nth root is a root extraction.

The nth root of x is written as ${\displaystyle {\sqrt[{n}]{x}}}$ using the radical symbol ${\displaystyle {\sqrt {\phantom {x}}}}$. The square root is usually written as ⁠${\displaystyle {\sqrt {x}}}$⁠, with the degree omitted. Taking the nth root of a number, for fixed ⁠${\displaystyle n}$⁠, is the inverse of raising a number to the nth power, and can be written as a fractional exponent: