If the square of a nonnegative X is equal to A, that is, X 2 = A, then this nonnegative X is called the arithmetic square root of A, and the arithmetic square root of A is marked as √a, which is pronounced as "root number A", and A is called radix. The operation of finding the square root of a non-negative number is called square root.

If a positive number has a square root, then there must be two, and it is reciprocal. Obviously, if we know one of these two square roots, we can get the other square root in time according to the concept of reciprocal.

In a real number system, negative numbers cannot be squared. Only in a complex system can negative numbers be squared. The square root of a negative number is the pure imaginary number of a pair of yokes. For example, the square root of-1 is I, and the square root of -9 is 3i, where I is an imaginary unit.

Extended data:

Definition of arithmetic square root:

If the square of a nonnegative X is equal to A, then this nonnegative X is called the arithmetic square root of A, which is denoted as X = √ A ... where A is called the root sign. For example, because the squares of 2 and -2 are both 4 and only 2 is a positive number, 2 is the arithmetic square root of 4.

Because the square roots of positive numbers are opposite, the square roots of positive numbers can be recorded as √a and -√a respectively, or as √a together. For example, the square root of 5 can be written as √5 and -√5 respectively, and can be written as √5 together.

Baidu encyclopedia-square root