bonanova 79 Report post Posted July 20, 2016 Can you find irrational numbers a and b such that a^{b} is a rational number? Share this post Link to post Share on other sites

1 DejMar 8 Report post Posted July 20, 2016 Spoiler One example of two irrational numbers a and b such that a^{b} 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. Share this post Link to post Share on other sites

1 mmiguel 1 Report post Posted July 20, 2016 Spoiler a = pi c = a^b = 2 b = ln(2)/ln(pi) Share this post Link to post Share on other sites

0 jasen 4 Report post Posted July 20, 2016 (edited) 3 hours ago, bonanova said: Can you find irrational numbers a and b such that a^{b} is a rational number? Spoiler ignore this Edited July 20, 2016 by jasen different view in handphone and computer Share this post Link to post Share on other sites

0 bonanova 79 Report post Posted July 21, 2016 Both good answers. Here's another. Spoiler b = sqrt(2). a = b^{b} a^{b} = (b^{b})^{b} = b^{(bxb) }= b^{2 }= 2 Share this post Link to post Share on other sites

Can you find irrational numbers

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