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What is "square root"

Longman Dictionary of Contemporary English
square root
noun
EXAMPLES FROM CORPUS
▪ A number of early computers had an instruction to extract a square root, but nowadays this operation is achieved by software.
▪ Does this have a square root?
▪ Excluding the few outliers, we can calculate the square root of the average squared error over all subjects for each repetition.
▪ Having a square root for-1, it is now no great effort to provide square roots for all the real numbers.
▪ The square root of it is two hundred and seventy-seven point four nine.
▪ Unfortunately, the question seemed to me something of a nonsense, as it involved the square root of a minus quantity.
Wiktionary
square root

n. (context mathematics English) Of a number, another number which, when squared, yields the original number; sometimes constrained to be the positive number when two solutions exist.

WordNet
square root

n. a number that when multiplied by itself equals a given number

Wikipedia
Square root

In mathematics, a square root of a number a is a number y such that ; in other words, a number y whose square (the result of multiplying the number by itself, or ) is a. For example, 4 and −4 are square roots of 16 because .

Every non-negative real number a has a unique non-negative square root, called the principal square root, which is denoted by , where √ is called the radical sign or radix. For example, the principal square root of 9 is 3, denoted = 3, because and 3 is non-negative. The term whose root is being considered is known as the radicand. The radicand is the number or expression underneath the radical sign, in this example 9.

Every positive number a has two square roots: , which is positive, and −, which is negative. Together, these two roots are denoted ± (see ± shorthand). Although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root. For positive a, the principal square root can also be written in exponent notation, as a.

Square roots of negative numbers can be discussed within the framework of complex numbers. More generally, square roots can be considered in any context in which a notion of "squaring" of some mathematical objects is defined (including algebras of matrices, endomorphism rings, etc.)