One I learned recently: E.g. sqrt(7) = 3 x sqrt(1-2/9) ~= 3 x (1 - (1/2)(2/9)) = 3 x 8/9 = 2.6667 Where the second line uses the first term of the binomial

One I learned recently: E.g. sqrt(7) = 3 x sqrt(1-2/9) ~= 3 x (1 - (1/2)(2/9)) = 3 x 8/9 = 2.6667 Where the second line uses the first term of the binomial series, i.e. (1+x)^(1/2) ~= 1+ x/2 Real answer is 2.65 in this case, obviously picking a factor to pull out that makes x as small as possible works best