In fact, Newton's method of opening is the application of Newton 's iterative method in square rooting. Newton's iterative method can also quickly approximate the solutions of many equations, and can naturally be used to open any square.
Seek is the positive root of 
seeking .
More generally, seeking is the positive root of 
seeking .
Note that the Newton iteration method can only approximate the solution and cannot calculate the exact solution. However, in practical applications, we do not require an absolutely accurate solution. For example, the calculator does not need to give infinite digits, only a dozen decimal places are enough, so the Newton iteration method is widely used in various in scientific computing.
[Newton iteration method]
Assuming that the equation 
has 
a root nearby, then using the following iterative formula: 
calculate 
, 
, 
, . .
The principle of the Newton iteration method is very simple. In fact, it estimates the intersection of f(x) and the x-axis according to the value and slope of f(x) near x0. See the following dynamic diagram:
[Square root with Newton's iteration method]
Let: 
So the first derivative of f(x) is: 
Newton iteration:
The initial value of any iteration, for example 
, is substituted into the above formula iteration.
For example calculation 
, i.e. a=2. 
...
available on the calculator
[Use Newton's iteration method to open any power]
The recursive formula required is: