How would you estimate square root of 1000?

Answer 1

Find perfect square routes above and below 1000.

31 x 31 = 961

32 X 32 = 1024

So if we take the two differences between the upper and lower values bracketing 1000 we get 39 below and 24 above so the ratio of 24/31 is about .6

So the number we are looking for is about 31.6