Calculation formula of square root of junior middle school mathematics
These simple and commonly used square root estimates can be calculated by pressing the calculator and then remembering. 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
What is a square root?
The square root is also called quadratic square root, which is expressed as √ ~ 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; The square root of a pure imaginary number with two yokes. [ 1]
Generally speaking, "√ ~" is only used to represent the arithmetic square root, that is, a non-negative square root. For example, the mathematical language is √ ~ 16 = 4. The language description is: root number 16=4 (also called root number 16=4).
Square root calculation steps
1. Divide the integer part of the square root into a section with two digits from the unit to the left, and separate it with apostrophes (vertically 1 1'56), indicating how many digits there are in the square root;
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.
The method of manually opening n times square root:
Principle: Let the number of roots be x, open n power, let the result of the previous step be a, now let's try the next bit of the root, set it as b,
There are: (10 * a+b) n-(10 * a) n.
The above is the formula for calculating the square root of junior high school mathematics, which I compiled for you. I hope it will help you! !