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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
List of Kangxi radicals － a system of 214 components used by the Kangxi dictionary (1716), made under the leadership of the Kangxi Emperor; List of Unicode radicals － CJK radicals included in the Unicode Standard. List of Xinhua Zidian radicals; Chinese characters description languages － computer and SVG based description of CJK ...
Reflection of the form of the radical (字型特徵) – the decomposition should reflect the shape of the radical, meaning (a) using the same code twice or more should be avoided if possible, and (b) the shape of the character should not be "cut" at a corner in the form.
In the case of two nested square roots, the following theorem completely solves the problem of denesting. [2]If a and c are rational numbers and c is not the square of a rational number, there are two rational numbers x and y such that + = if and only if is the square of a rational number d.
Thus, 6.25 = 110.01 in binary, normalised to 1.1001 × 2 2 an even power so the paired bits of the mantissa are 01, while .625 = 0.101 in binary normalises to 1.01 × 2 −1 an odd power so the adjustment is to 10.1 × 2 −2 and the paired bits are 10. Notice that the low order bit of the power is echoed in the high order bit of the pairwise ...
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}
Plot of the Bring radical for real argument. In algebra, the Bring radical or ultraradical of a real number a is the unique real root of the polynomial + +.. The Bring radical of a complex number a is either any of the five roots of the above polynomial (it is thus multi-valued), or a specific root, which is usually chosen such that the Bring radical is real-valued for real a and is an ...
The ring of radical polynomials is a graded subalgebra of the ring of all polynomials. The standard separation of variables theorem asserts that every polynomial can be expressed as a finite sum of terms, each term being a product of a radical polynomial and a harmonic polynomial .