Example 3: square roots (1)
A square root of a positive number a is a number r such that r2 = a.
Newton’s square-root algorithm:
To compute approximately the positive square root of a positive number a:
1. Set r to the mean of 1 and a.2. Until r2 is approximately equal to a, repeat: 2.1 Set r to the mean of r and a/r.3. Terminate with answer r.
Could be performed by a human, perhaps equipped with log tables or a calculator.