Posted by **excel** on Monday, February 17, 2014 at 11:15pm.

1a) Prove that there exist irrational numbers a and b so that a^b is rational. look at the numbers √2^√2 and (√2^√2)^√2

1b) use similar idea to prove that there exists a rational number a and an irrational number b so that a^b is irrational

1c) prove that if 2^√2is irrational then √2^√2is irrational.

Thanks for your help.

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