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.
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,
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