What is the arithmetic square root of 7?

The arithmetic square root of 7 is √7.

√7=2.64575 ...

√7≈2.6458 (accurate to 4 decimal places)

computing formula

1, √ AB = √ A √ B √ A ≥ 0B ≥ 0 √ This can be used interchangeably. This can be used for simplification at most, such as √ 8 = √ 4 √ 2 = 2 √ 2.

2、√a/b=√a÷√b﹙a≥0b﹥0﹚

3、√a？ =|a| (actually equal to absolute value) is the key and difficult point of quadratic root. When a > 0, √a? =a (equal to itself); When a=0 √a? =0; When a < 0, √a? =-a (equal to its reciprocal)

4. Denominators are physical and chemical: Denominators cannot have or contain quadratic roots. When the denominator has only one quadratic root, then the denominator of the numerator is multiplied by the same quadratic root at the same time by using the fractional property. If the denominator is √3, then the numerator denominator is multiplied by √3 at the same time.

Extended data

Calculation steps of square root

1. Divide the integer part of the square root into a paragraph every two bits from the unit to the left, and separate it with apostrophes (vertical type is 1 1'56), indicating how many bits 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 (20×3 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 digits of the square root.

In the case of infinite opening, the approximate value can be obtained according to the required accuracy. For example, the approximate value (accurate to 0.0 1) can be listed in the vertical table at the upper right of the above figure, and it can be obtained according to this vertical table.

It is complicated to calculate the square root with words, but it is rarely used directly in practice. However, this method can be used to approximate the square root of a number with arbitrary accuracy.

References:

Baidu Encyclopedia-Square Root Operation