To know which numerical method to use for a problem one first needs to understand the various methods and evaluate the problems.
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When you construct and use a table to solve a problem, you are using a numerical approach.
Numerical Methods are used because of following reasons> 1. NO analytical solution of a problem exists. 2. Analytical solution exists but is difficult to find. 3. Due to use of computers, cumbersome calculations can be done easily and solution is reached in shorter duration of time.
Decide which method you will use to solve the problem.
If a person doesn't know the proper method to solve a problem or any shortcuts, brute force is the only method he can use, which might help him make an educated guess.
There are a number of ways. The simplest would be to use a calculator (you probably would not know how to use log tables or a slide rule!) You could find a square root graphically; use numerical methods such as the Newton-Raphson method (not very fast but simple). There is also a method similar to long division, but that is rather complicated.