Near a root Newton's method roughly doubles the number of correct digits at each step. Starting from a guess with 1 correct digit, how many correct digits should you expect after 3 steps?

8

1, 2, 4, 8, quadratic convergence. Bisection would have gained roughly one binary digit per step over the same three steps, which is the concrete meaning of 'quadratic beats linear' once you are close enough for Newton to be safe.