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Radical 68 or radical dipper (斗部) meaning "dipper" is one of the 34 Kangxi radicals (214 radicals in total) composed of 4 strokes. In the Kangxi Dictionary , there are 32 characters (out of 49,030) to be found under this radical .
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 ...
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
An unresolved root, especially one using the radical symbol, is sometimes referred to as a surd [2] or a radical. [3] Any expression containing a radical, whether it is a square root, a cube root, or a higher root, is called a radical expression, and if it contains no transcendental functions or transcendental numbers it is called an algebraic ...
Radical expression involving roots, also known as an nth root; Radical symbol (√), used to indicate the square root and other roots; Radical of an algebraic group, a concept in algebraic group theory; Radical of an ideal, an important concept in abstract algebra; Radical of a ring, an ideal of "bad" elements of a ring
Algebraic expressions may be evaluated and simplified, based on the basic properties of arithmetic operations (addition, subtraction, multiplication, division and exponentiation). For example, For example,
'Chinese character radicals table') is a lexicographic tool used to order the Chinese characters in mainland China. The specification is also known as GF 0011-2009 . In China's normative documents, "radical" is defined as any component or 偏旁 piānpáng of Chinese characters, while 部首 is translated as "indexing component".
They may also be performed, in a similar way, on variables, algebraic expressions, [2] and more generally, on elements of algebraic structures, such as groups and fields. [3] An algebraic operation may also be defined more generally as a function from a Cartesian power of a given set to the same set.