First we define the function and compute the derivative.

Now set up the Newton's Method recurrence.

Now we set the initial value.

Now we can find repeated approximations just by evaluating the next box as many times as we want.

We can check accuracy at any time. To check if 2.24 is correct to 2 decimal places, for example, we compute $f(2.24-.005)$, and $f(2.24+.005)$, to see if one of them has a different sign than $f(2.24)$.