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I don't know how to do this I'm just curious how can I.

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  • $\begingroup$ Do you have any thoughts on this? People are more likely to answer if they can see you have put in some effort yourself $\endgroup$
    – lioness99a
    Mar 2, 2020 at 11:00

1 Answer 1

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Let $x$ and $y$ be 2 real numbers. Choose $y = \sqrt{2}$ and $x = \sqrt{3}^{\sqrt{2}}$

Now there are two scenarios possible :-

  1. $x$ is rational, in which case your proposition is proved, as x is a number which equals an irrational number raised to the power of another irrational number.

  2. $x$ is irrational, in which case we have $x^y = 3$ being rational.

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