The calculator's manual explains these features in detail. If your school acutally encourages the use of calculators, then you could always ask your instructors how to use the calculator. In addition, Ray Kremer's FAQ lists various tips regarding math functions of the calculator.
If you are having difficulty using the calculator for math, it might help to try thinking about the math problem in a different way rather than wondering about the calculator.
This question is actually a perfect example of what I mentioned in the last question. Computing the nth root of a number is the same as raising the number to the (1/n) power. So, if you need to find the 3rd (cube) root of 125, for example, you would type "125^(1/3)".
There is no one single source for such programs, but you could try the following sites:
Note, however, that the built-in math features of the calculator usually do much more than these programs. In many cases, the things that you might want a program to do (and which many programs have been written to do) could easily be done by hand or by using one or two of the built-in operations the calculator does. Most of the truly advanced math and science programs are on the TI-89/92/92+, though a few useful ones are available for the others (many of those under development are 83+ flash applications).
Of course not! Shame on you for even thinking such a thing!