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Square root. Notation for the (principal) square root of x. For example, √ 25 = 5, since 25 = 5 ⋅ 5, or 52 (5 squared). In mathematics, a square root of a number x is a number y such that ; in other words, a number y whose square (the result of multiplying the number by itself, or ) is x. [1] For example, 4 and −4 are square roots of 16 ...
In mathematics, taking the nth root is an operation involving two numbers, the radicand and the index or degree. Taking the nth root is written as , where x is the radicand and n is the index (also sometimes called the degree). This is pronounced as "the nth root of x". The definition then of an nth root of a number x is a number r (the root ...
Radical symbol. In mathematics, the radical symbol, radical sign, root symbol, radix, or surd is a symbol for the square root or higher-order root of a number. The square root of a number x is written as. while the n th root of x is written as. It is also used for other meanings in more advanced mathematics, such as the radical of an ideal .
Digital root. The digital root (also repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached.
Algebraic number. The square root of 2 is an algebraic number equal to the length of the hypotenuse of a right triangle with legs of length 1. An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, , is an algebraic number ...
An n th root of unity, where n is a positive integer, is a number z satisfying the equation z n = 1. {\displaystyle z^{n}=1.} Unless otherwise specified, the roots of unity may be taken to be complex numbers (including the number 1, and the number −1 if n is even , which are complex with a zero imaginary part ), and in this case, the n th ...
The shifting n th root algorithm is a generalization of this method. Basic principle. First, consider the case of finding the square root of a number Z, that is the square of a two-digit number XY, where X is the tens digit and Y is the units digit. Specifically:
In particular, if the number of sign changes is zero or one, the number of positive roots equals the number of sign changes. Negative roots. As a corollary of the rule, the number of negative roots is the number of sign changes after multiplying the coefficients of odd-power terms by −1, or fewer than it by an even number. This procedure is ...