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prove that root 2 power root 2 is irrational .

Mathematics
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|dw:1358647793062:dw|
yep
Well since root 2 is irrational, an irrational number raised to an irrational number should still be irrational.

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Other answers:

But that's not always true. Hmm... Intresting. One moment.
Thing is, this is NOT an irrational number. It's rational.
Use proof by contradiction.
Assume is IS rational.
ok go on
i dont have a very nice method but i guess this will help you let's say \[x= 2 ^{\sqrt2}\] take log on both the sides \[\log x = \sqrt {2}\log2\] find the value of right side and finally \[X= e ^{\sqrt2 \log 2}\] and i am sure that would be irrational
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you need to use calculator
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This is obviously rational.
^ two.. not 4
Right. Still rational though.
there is a fallacy as far as i can see in your solution that you have missed square root on the exponent @djdo525
sorry its Dido
ok guys one correction, that root 2 power root 2 is rational . Sorry But prove that root 2 power root 2 is transcendental
Also, PLEASE check whether it is transcendental or not , I am not sure. But I need your help.
lol that was horrible
OK friends I am totally confused. http://www.math.hmc.edu/funfacts/ffiles/30002.3-5.shtml Here I got that root 2 power root 2 is irrational..
^ and as well as transcendental
@Dido525 , your example is incorrect, you showed (sqrt2)^(sqrt2)^sqrt2 is rational but sqrt2^sqrt2 is irrational
yep
Yeah. That's what he wanted.

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