This is not accurate square root and is just approximation for example the square root of three will be 1.75 according to this approach which is not correct. You should also mention the limitation of this method.
How can you do if you do not know the nearest square for bigger numbers? Like that 576 square root. Someone said memorise square upto 30. But for even bigger numbers. And division of small numbers by larger products is slow and tedious. That fraction trick you do on the side is like a true but it's not common knowledge. Please tell me there's an easier way. And without a calculator. Edit: that being said, I appreciate you helping us out. Thank you.