bonanova Posted July 20, 2016 Report Share Posted July 20, 2016 Can you find irrational numbers a and b such that ab is a rational number? Quote Link to comment Share on other sites More sharing options...
1 DejMar Posted July 20, 2016 Report Share Posted July 20, 2016 Spoiler One example of two irrational numbers a and b such that ab is rational is where a = √10 and b = log(4). Both √10 and log(4) are known to be irrational numbers, yet (√10)log(4) = (10)log(2) = 2, and 2 is definitely rational. Quote Link to comment Share on other sites More sharing options...
1 mmiguel Posted July 20, 2016 Report Share Posted July 20, 2016 Spoiler a = pi c = a^b = 2 b = ln(2)/ln(pi) Quote Link to comment Share on other sites More sharing options...
0 jasen Posted July 20, 2016 Report Share Posted July 20, 2016 (edited) 3 hours ago, bonanova said: Can you find irrational numbers a and b such that ab is a rational number? Spoiler ignore this Edited July 20, 2016 by jasen different view in handphone and computer Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted July 21, 2016 Author Report Share Posted July 21, 2016 Both good answers. Here's another. Spoiler b = sqrt(2). a = bb ab = (bb)b = b(bxb) = b2 = 2 Quote Link to comment Share on other sites More sharing options...
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bonanova
Can you find irrational numbers a and b such that ab is a rational number?
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