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.