Question: What is Trial and Improvement ?


This is a method for obtaining a solution to a problem by making a succession of trials based on the results of the previous trials to get nearer to the required result.

Suppose for example, we want to find a number x so that x2 lies between 29.5 and 30. we know that 52 = 25 and that 62 = 36, so we make a first trial guess 5.5 and find that 5.52 = 30.25. So 5.5 is too large, suggesting a next trial of 5.4, giving 5.42 = 29.16 which is too small. The third trial is now made between the other two with 5.45, giving 5.452 = 29.7025. This lies between 29.5 and 30 as required so no further trials are needed. If the gap had been 29.5 to 29.6 then further trials would be needed.