I estimate square roots by just imagining a square. The area of tyhe square is the thing you are square rooting, the sides of the square are the roots. Eg, wahts the square root of 2345. Well roughly imagine a square of Area 2300, the sides are bigger than 100 (1/2 as big), but not more than 200 which would be 2x too big, so its probably around 150.
Well, considering 100 * 100 is clearly more than 4 times 2300 its more an error of my basic mulitplication than my method of estimating squares. Was just focused on something else at the time of writing (as indicated by the spelling). Considering that a square root by definition is the side of the square described, visualising it sure doesn't hurt.
If I tried again I'd say 100* 100 = 10,000, 1010 = 100, 50 50 = 2500, so that going to be pretty close. 48 is pretty close to 50.
