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In mathematics, a square root of a number x is a number y such that ; in other words, a number y whose square (the result of multiplying the number by itself, or ) is x. [1] For example, 4 and −4 are square roots of 16 because .
Using the multiplication tables embedded in the rods, multiplication can be reduced to addition operations and division to subtractions. Advanced use of the rods can extract square roots. Napier's bones are not the same as logarithms, with which Napier's name is also associated, but are based on dissected multiplication tables.
Methods of computing square roots are algorithms for approximating the non-negative square root of a positive real number . Since all square roots of natural numbers, other than of perfect squares, are irrational, [1] square roots can usually only be computed to some finite precision: these methods typically construct a series of increasingly accurate approximations .
Further reading. Computational complexity of mathematical operations. Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations .
In mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix product BB is equal to A. [1]
The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself or squared, equals the number 2. It may be written in mathematics as or . It is an algebraic number, and therefore not a transcendental number. Technically, it should be called the principal square root of 2, to distinguish it from the negative number with the same property.
Napier coined the word rabdology (from Greek ῥάβδος [rhabdos], rod and λόγoς [logos] calculation or reckoning) to describe this technique. The rods were used to multiply, divide and even find the square roots and cube roots of numbers. The second device was a promptuary (Latin promptuarium meaning storehouse) and consisted of a large ...
Move one of the counters in each row of the square to the margin and the positions of these marginal counters will yield the square root of the number. Example of finding the square root of 1238 using Napier's method for finding square roots provided in Rabdology on page 151. Napier provides an example of determining the square root of 1238.
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