> Substituting our values into this formula, we get: x1 = (3 + (10 / 3)) / 2 = 5

This is really wrong, why didn't the poster notice this? They just said

> 3.4 is not a very good approximation but other than that the response is correct.

No, Newtons method produces a really good approximation for square root very quickly, ChatGPT didn't do the method correctly which is why the result is so bad. People who can't instantly spot those mistakes shouldn't use ChatGPT, and people who can spot them instantly doesn't need to use ChatGPT.