The formula for calculating the square root of junior high school mathematics: X(n+ 1)=Xn+(A/Xn? Xn) 1/2. The square root is also called quadratic square root, which is expressed by √, and the square root that belongs to non-negative number is called arithmetic square root. Positive numbers have two real square roots in opposite directions; 0 has only one square root, which is 0 itself, and negative numbers have two pure imaginary square roots of * * * yokes.

These simple and commonly used square root estimates can be calculated by pressing the calculator and then remembering it. If you can't remember or are too lazy to remember, there are still ways to do it yourself. For example, ancient people without calculators calculated this way:

Suppose you need the square root of a, first assume that it is X, and then calculate (a/x+x)/2. Take the obtained number as X, and also calculate (a/x+x)/2 until the two numbers are almost equal.

For example, calculate √3, I assume it is 1.5,

Substituting into the above formula, (3/1.5+1.5)/2 =1.75,

Let me calculate again (3/1.75+1.75)/2 =1.732,

I continue to calculate (3/1.732+1.732)/2 =1.732,

They are the same, so keeping three decimal places is 1.732.

Press the calculator and you will get 1. 56438 . 6866868666 1

Square root calculation steps 1. Divide the integer part of the square root into a segment every two digits from the unit to the left, and separate it with apostrophes (vertically 1 1'56), and divide it into several segments, indicating how many digits the square root has;

2. According to the number in the first paragraph on the left, find the number at the highest square root (3 in vertical form);

3. Subtract the square of the highest digit from the number in the first paragraph, and write the number in the second paragraph to the right of their difference to form the first remainder (256 vertically);

4. Multiply the highest digit by 20 and try to divide by the first remainder, and the largest integer is the trial quotient (3×20 divided by 256, the largest integer is 4, that is, the trial quotient is 4);

5. Multiply the quotient by 20 times the highest digit of the quotient, and then multiply the quotient. If the product is less than or equal to the remainder, the quotient is the second digit of the square root; If the product is greater than the remainder, try again by subtracting the quotient ((20×3+4)×4=256 in vertical form, indicating that quotient 4 is the second place of the square root);

6. In the same way, continue to look for numbers on other bits of the square root.