trial and improvement method

In mathematics, method of problem solving that uses a series of estimations, getting closer and closer to the actual answer. For example, when calculating √10, the answer must lie between 3 and 4, because 32 = 9 and 42 = 16. So a first guess might be 3.5:

3.52 = 12.25 – too large, so improve the guess; 3.22 = 10.24 – too large; 3.12 = 9.61 – too small; 3.152 = 9.9225 – too small; 3.172 = 10.0489 – too large; 3.162 = 9.9856 – too small; 3.1652 = 10.017225 – too large; 3.1642 = 10.010896

The final answer, 3.164, although still too large, is probably accurate enough for most purposes. The problem solver does not expect to solve the problem outright but only to get progressively nearer to a solution.