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Hello! When in doubt, please ask.
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For example, 1156 is a four-digit number, so it's the square root of arithmetic.
The integer part of is a two-digit number, and it is easy to observe that the ten digits are 3. So the crux of the question is: how do you find its single digit a? To do this, let's start with the relational formula that A satisfies.
According to the formula of the sum of two numbers, it can be obtained.
1156=(30+a) 2=30 2+2 30a+a 2, so 1156 30 2=2 30a+a 2, i.e. 256=(30 2+a)a, i.e., a is such a positive integer.
It is the sum of 30 2, multiplied by itself, equal to 256.
In order to find a, the following vertical formula can be used to calculate:
The number 3 above the root number is the ten-digit number of the square shouting with the root. Divide 256 by 30 2 to get 4 (if not divided, take the whole number).Since the sum of 4 and 30 2 is 64, and the product of 4 is equal to 256, 4 is the single digit a sought. The remainder in the vertical type.
is 0, which means that the opening is just at the end of the opening. So we get 1156=34 2, or 1156=34The above method of finding the square root is called the pen calculation method of opening the level, with this method you can find the arithmetic square root of any positive number, and its calculation steps are as follows:
Calculation steps for prescribing.
1 divides the integer part of the square number from the unit digit to the left every two digits in a paragraph, with ".'This symbol is divided (11'56 in vertical) into segments, indicating that the square root sought is a few digits;
2 According to the number in the first paragraph on the left, find the number in the highest digit of the square root (3 in the vertical formula);
3 Subtract the square of the number in the highest position from the number in the first segment, and write the number of the second segment to the right of their difference to form the first remainder (256 in vertical);
4 Multiply the highest digit by 20 to divide the first remainder, and the largest integer obtained is used as the test quotient (20 3 divided by 256, the maximum integer obtained is 4, so the test quotient is 4);
5 Use 20 times the highest digit of the quotient plus this quotient and multiply it by the quotient, if the resulting product is less than or equal to the remainder, the quotient is the second digit of the square root; If the product obtained is greater than the remainder, try again after decreasing the test quotient (in the vertical formula, (20 3+4) 4=256, indicating that the test quotient 4 is the second digit of the square root);
6 In the same way, continue to find the number on the rest of the square roots.
In the case of incomplete opening, the required accuracy can be used.
Find its approximate value. For example, find its approximate value (to be accurate, you can list the vertical style of the right side of the smile above, and get it according to this vertical style.
Pen arithmetic open square operation.
It is more complex and has few direct applications in practice, but this method can be used to find an approximation of the square root of a number with arbitrary precision.
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, the side of the finch circle 5 is the approximate square root of the collapse technique;
They are236;
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Ratio 2 is equal to 4 points, and the accompaniment of the pants is equal to 11, and the ratio of (4) is equal to 12 points (33) is equal to (. In the case of Luxi: (Ratio 2 is equal to 1/4 is equal to (1) Ratio (4) is equal to 12/12 (3) is equal to (.)
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【Analysis】 First of all, according to the meaning of the square root, we know that there are two solutions to each problem. Secondly, if the result is an approximate value, three decimal places are retained, that is, four decimal places are taken, and the value of the third decimal place is determined by rounding. 1) The approximation of the square root of n, i.e., 14, is ; n(2) n, i.e., the approximate square root is ; n(3) The approximate value of the square root of n is Comments] When using a calculator to find the square root, pay attention to the order of the keys.
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