[HungLikeJesus]

I realized this morning while I was eating breakfast that if you know that the square root of a number, a, is b, the square root of (a+2) is very close to (b+1/b).

For example, the square root of 100 is 10, so the square root of 102 is approximately 10 + 1/10 (10.1 squared is 102.01).

Also, the square root of (a+1) is very close to (b + 1/(2*b)). -> The square root of 101 is approximately (10 + 1/20) = 10.05.

This makes it easy to calculate square roots for numbers close to known squares.

This is less accurate for small numbers, the error being (1/b) squared in the first case and 1/(4b^2) in the second case.