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A positive number has two square roots, one positive, and one negative, which are opposite to each other. When talking of the square root of a positive integer, it is usually the positive square root that is meant. The square roots of an integer are algebraic integers—more specifically quadratic integers.
A square root of a number x is a number r which, when squared, becomes x: =. Every positive real number has two square roots, one positive and one negative. For example, the two square roots of 25 are 5 and −5. The positive square root is also known as the principal square root, and is denoted with a radical sign:
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. For the definition of the principal square root of other complex numbers, see Square root § Principal square root of a complex number.
The principal square root of a real positive semidefinite matrix is real. [3] The principal square root of a positive definite matrix is positive definite; more generally, the rank of the principal square root of A is the same as the rank of A. [3] The operation of taking the principal square root is continuous on this set of matrices. [4]
Methods of computing square roots are algorithms for approximating the non-negative square root of a positive real number. Since all square roots of natural numbers , other than of perfect squares , are irrational , [ 1 ] square roots can usually only be computed to some finite precision: these methods typically construct a series of ...
Negative numbers: Real numbers that are less than zero. Because zero itself has no sign, neither the positive numbers nor the negative numbers include zero. When zero is a possibility, the following terms are often used: Non-negative numbers: Real numbers that are greater than or equal to zero. Thus a non-negative number is either zero or positive.
A more familiar principal branch function, limited to real numbers, is that of a positive real number raised to the power of 1/2. For example, take the relation y = x 1/2, where x is any positive real number. This relation can be satisfied by any value of y equal to a square root of x (either positive or negative).
The square root of 2 (approximately 1.4142) is the positive real number that, ... to distinguish it from the negative number with the same property.