If the square of x is equal to a, then x is called the square root of a.

The operation of finding the square root of a number is called square root, and the square and square root are reciprocal operations.

The sign of the square root of a(a≥0) is √a (a ≥ 0), where √a is the arithmetic square root of a (the root sign can't be entered by computer, here is just a sign. Please refer to the representation of the root sign in the lecture. )

Key point explanation

When the formula √a is meaningful, a must represent a non-negative number, that is, √a≥0 and a≥0.

The difference between square root and arithmetic square root

2, the difference:

(1) has different definitions; (2) The results are different;

3. Contact person:

(1) square root contains arithmetic square root;

(2) The number of roots is non-negative;

(3) The square root and arithmetic square root of 0 are both 0.

Key point explanation

(1) A positive number has two square roots, the two square roots are in opposite directions, and the positive one is called its arithmetic square root; Negative numbers have no square root.

(2) The two square roots of a positive number are opposite, and the other square root can be written immediately according to its arithmetic square root. Therefore, we can use the arithmetic square root to study the square root.

4. The nature of square root

5. Square Root Decimal Shift Law

If the decimal point of the root sign is moved to the right or left by 2 digits, the decimal point of its arithmetic square root is correspondingly moved to the right or left by 1 digit. For example: