Search results
Results From The WOW.Com Content Network
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}
A non-nested radical expression is said to be in simplified form if no factor of the radicand can be written as a power greater than or equal to the index; there are no fractions inside the radical sign; and there are no radicals in the denominator.
There are 252 points on the surface of a cuboctahedron of radius five in the face-centered cubic lattice, [8] 252 ways of writing the number 4 as a sum of six squares of integers, [9] 252 ways of choosing four squares from a 4×4 chessboard up to reflections and rotations, [10] and 252 ways of placing three pieces on a Connect Four board. [11]
The radical symbol refers to the principal value of the square root function called the principal square root, which is the positive one. The two square roots of a negative number are both imaginary numbers , and the square root symbol refers to the principal square root, the one with a positive imaginary part.
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.
Placed on the right, as in 都 (dū "metropolis", also read as dōu "all"), it represents an abbreviated form of 邑 yì "city"; placed on the left, as in 陸 lù "land", it represents an abbreviated radical form of 阜 fù "mound, hill". Some of the most important variant combining forms (besides 邑 → 阝 and 阜 → 阝per the above) are:
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.).
Chinese characters "Chinese character" written in traditional (left) and simplified (right) forms Script type Logographic Time period c. 13th century BCE – present Direction Left-to-right Top-to-bottom, columns right-to-left Languages Chinese Japanese Korean Vietnamese Zhuang (among others) Related scripts Parent systems (Proto-writing) Chinese characters Child systems Bopomofo Jurchen ...