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: under the root number 16=4 (also called root number 16=4).
describe
Like addition, subtraction, multiplication and division, square root has its own vertical algorithm. calculate
For example. The process is as follows: finally, find out.
It is approximately equal to 1.732 (three decimal places are reserved).
Process 1
Because each complement needs to add two digits, when the root number exceeds one digit, make sure that the complement can't clip the decimal point. For example, three digits must be operated separately from hundreds, and ten digits and one digit are added when complement is added.
Process 2
Each transition number is changed by the last transition number, and then the single digits of the last transition number are multiplied by 2. If carry is needed, advance 1, then increase the unit number by ten digits, and so on, and add the new operand to the unit number. Simply put, the transition number 27 is 1 of the first quotient multiplied by 20, and 7 of the second quotient replaces the unit 0. Transition number 343 is 17 of the first two quotients multiplied by 20=340, where unit 0 is replaced by 3 of the third quotients, and the third transition number 3462 is 173 of the first three quotients.
Process 3
The role of error value. If you need to be accurate to a higher number of decimal places, you can continue to calculate the error value according to the rules.
example
Calculate √ 10
3. 1 6 2 2 7 -
-
√ 10'00'00'00'00' -
3| 9 3 1 3
-
6 1 |1002 * 3 *10+1= 612nd place1
| 6 1
-
626 | 3900 2 * 31*10+6 = 626 Third place 6
| 3756
-
6322 |14400 2 * 316 *10+2 = 6322 4th bit 2
| 12644
-
63242| 175600
| 126484
-
632447|49 1 1600
|4427 129
-
××××××× 00 (and so on)
So, √ 10=3. 16227…
Another example is 7.
= 2.6 4 5 …
-
2 | 7
four
-
4 6 |300
276
-
52 4 | 2400
2096
-
528 5 | 30400
26425
-
5290? | 3 9 75 00