Irrational numbers operating on irrational numbers



I have wondered if irrational numbers could operate on irrational numbers to produce a rational number.  How to find which two rational numbers will produce a rational number?  Only one irrational number is needed and any rational number can be chosen.For two irrational numbers and one rational number:
i1 X i2 = R
i1 X (R / i1) = Rπ X (5 / π) = 5π X 1.5915494309… = 5
2 3 = 8
8 1/3 =2
(8 1/3) 3 = 8
(13 1/π) π = 13
2.2624509981… π = 13




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