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A solution in radicals or algebraic solution is an expression of a solution of a polynomial equation that is algebraic, that is, relies only on addition, subtraction, multiplication, division, raising to integer powers, and extraction of n th roots (square roots, cube roots, etc.). A well-known example is the quadratic formula
The nested radicals in this solution cannot in general be simplified unless the cubic equation has at least one rational solution. Indeed, if the cubic has three irrational but real solutions, we have the casus irreducibilis, in which all three real solutions are written in terms of cube roots of complex numbers. On the other hand, consider the ...
In number theory, the radical of a positive integer n is defined as the product of the distinct prime numbers dividing n. Each prime factor of n occurs exactly once as a factor of this product: r a d ( n ) = ∏ p ∣ n p prime p {\displaystyle \displaystyle \mathrm {rad} (n)=\prod _{\scriptstyle p\mid n \atop p{\text{ prime}}}p}
The symbol was first seen in print without the vinculum (the horizontal "bar" over the numbers inside the radical symbol) in the year 1525 in Die Coss by Christoff Rudolff, a German mathematician. In 1637 Descartes was the first to unite the German radical sign √ with the vinculum to create the radical symbol in common use today. [3]
In the Kangxi Dictionary, there are 37 characters (out of 49,030) to be found under this radical. In the Table of Indexing Chinese Character Components predominantly adopted by Simplified Chinese dictionaries published in mainland China , this radical is merged to radical sun ( 日 ) as an associated indexing component.
This is a simplified table of Japanese kanji visual components that does away with all the archaic forms found in the Japanese version of the Kangxi radicals.. The 214 Kanji radicals are technically classifiers as they are not always etymologically correct, [1] but since linguistics uses that word in the sense of "classifying" nouns (such as in counter words), dictionaries commonly call the ...
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