Originally Posted by

**MathCrusader** Q: Use Newton's method to approximate $\displaystyle \sqrt{10}$.

I know that "you are supposed to" let

$\displaystyle f(x) = x^2 - 10 \, ,$

and from there on proceed with Newton's method. I was wondering why we one cannot instead let

$\displaystyle f(x) = x - \sqrt{10} \, ?$

I realized that it is to no avail once you plug it all in into

$\displaystyle x_{n+1} = x_n - \frac {f(x_n)}{f'(x_n)} \, ,$

but I am not understanding *why* it would be wrong to let $\displaystyle f(x) = x - \sqrt {10}$. Is it merely because the sought value is not an intersection with the x-axis for $\displaystyle f(x) = x - \sqrt {10}$?