root
Quick Summary
In mathematics, a square root of a number is a value that, when multiplied by itself, yields the original number. For instance, both 3 and -3 are square roots of 9. The concept of roots extends to finding solutions for equations, where a root is a value that satisfies the equation. The nth root of a number a is written as n√a, with the square root being the case where n=2, denoted as √a. The third power of a quantity is called its cube, and the number that produces this cube is the cube root. For example, 3 is the cube root of 27 because 3³ = 27.123
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algebraThe equation in India and China…and solving quadratic equations by radicals—solutions that contain only combinations of the most tractable operations: addition, subtraction, multiplication, division, and taking roots. They were unsuccessful, however, in their attempts to obtain exact solutions to higher-degree equations. Instead, they developed approximation methods of high accuracy, such as those described in Yang…
Read More…and solving quadratic equations by radicals—solutions that contain only combinations of the most tractable operations: addition, subtraction, multiplication, division, and taking roots. They were unsuccessful, however, in their attempts to obtain exact solutions to higher-degree equations. Instead, they developed approximation methods of high accuracy, such as those described in Yang…
Read More- algebraImpasse with radical methods
…the impossibility of obtaining a radical solution for general equations beyond the fourth degree. He adumbrated in his work the notion of a group of permutations of the roots of an equation and worked out some basic properties. Ruffini’s proofs, however, contained several significant gaps.
Read More…the impossibility of obtaining a radical solution for general equations beyond the fourth degree. He adumbrated in his work the notion of a group of permutations of the roots of an equation and worked out some basic properties. Ruffini’s proofs, however, contained several significant gaps.
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East Asian mathematicsTheory of root extraction and equationsResearch appears to have resumed in the 11th century with the reediting of the “Ten Classics” and the production of new commentaries. Within this context new developments took place in branches of mathematics that had been explored at least since The…
Read MoreResearch appears to have resumed in the 11th century with the reediting of the “Ten Classics” and the production of new commentaries. Within this context new developments took place in branches of mathematics that had been explored at least since The…
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mathematicsMathematics in the 10th century…ways: by the extension of root-extraction procedures, known to Hindus and Greeks only for square and cube roots, to roots of higher degree and by the extension of the Hindu decimal system for whole numbers to include decimal fractions. These fractions appear simply as computational devices in the work of…
Read More…ways: by the extension of root-extraction procedures, known to Hindus and Greeks only for square and cube roots, to roots of higher degree and by the extension of the Hindu decimal system for whole numbers to include decimal fractions. These fractions appear simply as computational devices in the work of…
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