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What is square root?
The square root of a number is a smaller number that can be multiplied by itself to create the original number. For instance, 4 and −4 are square roots of 16, because 42 = (−4)2 = 16. Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by√x where the symbol√is called the radix or radical sign.
For instance, we write √9 = 3 in order to express the fact that the principal square root of 9 equals 3. The term or number of which square root is being considered is known as the radicand. The radicand is the expression or number underneath the radical sign, in this case, 9. For nonnegative x, the principal square root can also be written in exponent notation, as x1/2.
Every positive number x has two square roots: positive √x, and negative -√x. The two roots can be written more concisely using the ± sign as ±√x. The designation“the square root” is often used to refer to the principal square root although the principal square root of a positive number is only one of its two square roots.
Negative numbers of square roots can be discussed in the context of complex numbers. generally, square roots can be considered in any context in which a notion of the “square” of a mathematical object is defined. These contain square matrices and function spaces among other mathematical structures.
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Properties and uses
The principal square root function ƒ(x) = √x [usually just referred to as the “square root function”] is a function that maps the set of nonnegative real numbers onto itself. The square root function maps the area of a square to its side length in geometrical terms.
The square root of x is rational if and only if x is a rational number that can be represented as a ratio of two perfect squares [Check out the square root of 2 for confirmation that this is an irrational number and quadratic irrational for a confirmation for all non-square natural numbers]. The square root function maps rational numbers into algebraic numbers, which is a superset of rational numbers.