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Irrational to Rational

When will the product of two square roots result in an integer if each of the individual square roots is not equal to an integer?                            


As you have come to expect, I have chosen to use a spreadsheet to analyze my problem.  I guess it is just easier to see many different iterations of the same problem in this form.  Either that or I have a secret infatuation with Excel.

Investigation/Exploration of the Problem

Initially, I set up a formula to test various numbers, then I recalled some of the basic properties of radicals.  Take a look at my explanation...Multiplication property of radicals.doc


So this tells me that if I multiply like radicals, I will eliminate the irrational part of my number.



Take a look at my spreadsheet and feel free to input values of your own where indicated.


Extensions of the Problem

After about 2 hours, I discovered that I only considered radicals.  But what about п (pi) or e, or any other nonterminating, nonrepeating decimal?

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