newton

√x
r(0) = x
r(n) = (r(n-1)^2 + x) / 2r(n-1)

√7
r(0) = 7
r(1) = (7*7 + 7) / (2*7) = 4
r(2) = (4*4 + 7) / (2*4) = 2.875
r(3) = (2.875*2.875 + 7) / (2*2.875) = 2.654891304
r(4) = (2.654891304*2.654891304 + 7) / (2*2.654891304) = 2.645767044
r(5) = (2.645767044*2.645767044 + 7) / (2*2.645767044) = 2.645751311
r(6) = (2.645751311*2.645751311 + 7) / (2*2.645751311) = 2.645751311