We can actually make this approximation to the root of f(x) even better by repeating what we have just done but using the latest estimate \( x_1=2.25= \frac{9}{4} \nonumber\), a number that is even cl...We can actually make this approximation to the root of f(x) even better by repeating what we have just done but using the latest estimate \( x_1=2.25= \frac{9}{4} \nonumber\), a number that is even closer to the actual value of \( \sqrt{5} \nonumber\). We could continue this process generating a better approximation to \( \sqrt{5} \nonumber\), as shown in the table, where the last estimate approximates the correct answer to 5 places.
