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bonanova

Powerful rational number?

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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.

 

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3 hours ago, bonanova said:

Can you find irrational numbers a and b such that ab is a rational number?

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ignore this

Edited by jasen
different view in handphone and computer

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Both good answers. Here's another.
 

Spoiler

b = sqrt(2).

a = bb

ab = (bb)b = b(bxb) = b2 = 2

 

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