$g(x) = \frac{1}{2}(x - \frac{a}{x^2})$, $a > 1$ and $a<100$, if $a>0$ then $1<10^{2k}a<100$. So that
$\sqrt{a}=\sqrt{10^{-2k}10^{2k}a} = 10^{-k}\sqrt{10^{2k}a}$.
$x_0 = \min(a,10)$, $\forall a >0 $ $\exists k \in Z$ so that $10^{2k}a \in [1,100]$.
How can i find the number of iterations for Newton's method to find $\sqrt{a}$ with accuracy $10^{-8}$? I need some pointer as of where to start this.