Square root of two

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You can take a square root as exponent, as with

You can see that

It is an irrational number. You can take this number as exponent, then you get

It is a transcendental number and is called the constant of Gelfond-Schneider. If you take the root of this, you see

Now we take √2, as exponent, and get

From a transcendental number emerges a natural number. That is rather unexpected.

Russian mathematician Alexander Gelfond (1906 - 1968) and German mathematician Theodor Schneider (1911 - 1988) investigated transcendental numbers.