I can. Newtons method is pretty easy to do in your head, but with larger numbers you need to be very careful not to mess it up. But on paper it's trivial.
No, I actually can, just not for arbitrarily large numbers. And 'paper' is just temp storage, not a tool. A tool in this case would be a sliderule or a calculator or an abacus. Long division requires pen and paper too if you want to 'show your work', just like I would have to show on paper how I did the square root of say 47515, you could simply choose not to believe me if I spat out the answer, but if I showed you step-by-step on paper and you followed every step you would either also conclude that it is correct, or alternatively that I had made a mistake.
That's why I think it is significant that chatgpt gets the addition spot on but gives a wrong answer to the square root problem. I can do better than that off the top of my head and I do not have access to the same computational resources that it has.
