Square root is a concept that we must master in high school mathematics, but its calculation requires certain skills, so the formula table has become a sharp weapon for many students to learn. In this paper, we will share a formula table about square root, hoping to help us better master this knowledge.
1, the square root of the single digit is itself, for example, √9=3.
2. When the ten digits are even, the hundred digits are equal to the sum of the ten digits and then divided by 2, and the unit number is 5, such as √324= 18√256= 16.
3. When the ten digits are odd, the hundred digits are equal to the ten digits plus 1 and then divided by 2, and the unit number is 5, such as √529=23√96 1=3 1.
4. For a number n, if its integer part is p, the square of p is less than n, and the square of (p+ 1) is greater than n, the approximate value can be obtained by Newton iteration method, and the formula is: X(n+ 1)=(Xn+N/Xn)/2, where X0=N/2.
Through the introduction of the above formula table, we can see that it is not so difficult to calculate the square root. Of course, these formulas are just tools to help us calculate quickly, and it needs more in-depth study and understanding to truly master the method of square root. I hope students can use this knowledge flexibly according to the actual situation and improve their mathematical thinking ability.
Newton iteration method
The method of writing a square mentioned above is given by most of us in the appendix of the textbook when we are at school, which is too troublesome to practice. We can take the following measures: for example, the number 136 16 1. First, we find a number close to the square root of 136 16 1. Choose any number, such as between 300 and 400, and choose 350 as the representative. Let's calculate 0.5 (350+136161/350), and the result is 369.5.
Then we calculate 0.5 (369.5+136161/369.5) and get 369.0003. We found that 369.5 and 369.0003 are almost the same, while 369? The number at the end is 1. We have reason to conclude that 369? = 136 16 1。