Problem 21: Close Enough for All Practical Purposes
This problem was taken from the First Annual Northeast Regional High School
Programming Contest Championship. The contest was held at Western New England
College on May 13, 1986.
This program is not that difficult. For those of you who are math phobic I believe you can
handle this. Remember the textbook is your best friend. It is filled with the answers you
seek.You are Columbo, Ellery Queen, Agatha Cristi, and Sherlock Holmes all wrapped into
one problem solving machine. C’mon, don’t tell me you never heard of Columbo. You can do it.
If you need to discuss this problem feel free to stop into my office. With help, you can
become independent.
The square root of a number A can be computed by successive approximations using the
iterative formula
Xn+1 = (1/2) ( Xn + A/Xn )
Starting with X1 = 1 as an initial approximation for the square root of A a new
approximation X is computed using the above formula. This new approximation, in turn,
can be substituted in the formula to compute a newer approximation of X. This process
can be continued until the square of the new approximation is close enough to A, that is
| X2 – A | < e
where e is the prescribed degree of accuracy.
Write a program to compute the square root of a number using the procedure described
above. The number and the level of accuracy will be specified as command line
arguments.
If the program was launched with the following command line,
bash> a.out
24
.001
the output of your program should be a line that states something like this
The square root of 24 is 4.899.
Failing to prepare is preparing to fail. Become more efficient. You can do it.
Have you done all the problems in your pre-calculus or calculus book yet?
It does not matter if the teacher assigned them or not. Do them anyways.
Keep a notebook of all solved problems.
Math is good. Physics is good. College Writing I is good.
Be courteous to your reader.