COMPUTE y = SQRT(2) NOTE: if y = SQRT(x) then x/y - y = 0 if y ~ SQRT(x) then x/y - y ~ 0 x = 2 y = 1 (1st guess) x/y - y = 2 - 1 = 1 (not good enough) y = (x/y + y)/2 = (2 + 1)/2 = 1.5 (2nd guess) x/y - y = 2/1.5 - 1.5 = -0.16... (not good enough) y = (x/y + y)/2 = (2/1.5 + 1.5)/2 = -1.4166... (3rd guess) x/y - y = 2/1.4166... - 1.4166... = -0.004... (not good enough) y = (x/y + y)/2 = (2/1.4166... + 1.4166...)/2 = 1.4142... (4th guess) x/y - y = 2/1.4142... - 1.4142... = -0.000004... (good enough)