眾所周知，計算機的基本數值演算法是加減乘除，甚至只是加減法。而次方和開根演算法都是由四則運算混合表示而成的，因而根號計算比四則運算要慢很多。無理數如√2的浮點數計算就是由牛頓迭代法得出的。牛頓迭代法是一種用於計算曲線方程根的精確演算法（尤其是冪函式方程），比二分法更加高效，因為它基於微分。

As we all know, basic numerical calculation in the computer is: addition, subtraction, multiplication and division.

Or even only the addition and subtraction. But the power and root algorithm is a complex combination of the four fundamental operations, so they are much slower. Irrational numbers such as √2 whose floating point is obtained by the Newton-Raphson method. Newton-Raphson method is a precise algorithm used to calculate the curvilinear equation (especiallypower function), it’s more efficient than Dichotomy because it is based on the differential.

以計算√x（精度e）為例的c語言函式：

A example using C language calculating √x with precision ’e’:

double abs_value(double x)

{

if(x<0)x=-x;

return x;

}

double sqrt_root(double x,double e)

{

double x0=1;

while(abs_value(x0*x0-x)>e)

X0=(x0+x/x0)/2;

return x0;

}