Find the square root of $N = AB$.

Question

Using Newton Raphson, show that root of the equation $N=AB$ is $$\sqrt {N}= \frac S4 + \frac NS, \text{ where } S=A+B.$$

Answer 1

HINTS:

As almagest pointed out, it is not true that $\sqrt N = S/4+N/S$. But it is true that $\sqrt N \approx S/4+N/S$, and we can see that by using the Newton method. It will be the first approximation in the algorithm, if you choose the initial guess $x_0$ right. So there are two things to do:

1. Find the function $f$ you want to find the root (i.e. the zero) of. That is $x=\sqrt N \implies f(x)=0$ should hold.
2. Make a first guess at the square root. It should be something that is a good guess for $A\approx B$.