<Dd> r n = (1 / 2) − x n h n (\ displaystyle r_ (n) = (1 / 2) - x_ (n) h_ (n)) </Dd> <Dd> x n + 1 = x n + x n r n (\ displaystyle x_ (n + 1) = x_ (n) + x_ (n) r_ (n)) </Dd> <Dd> h n + 1 = h n + h n r n (\ displaystyle h_ (n + 1) = h_ (n) + h_ (n) r_ (n)) </Dd> <P> until r i (\ displaystyle r_ (i)) is sufficiently close to 0, or a fixed number of iterations . </P>

By what method did the ancient babylonians approximate square roots