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Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Well since root 2 is irrational, an irrational number raised to an irrational number should still be irrational.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1But that's not always true. Hmm... Intresting. One moment.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Thing is, this is NOT an irrational number. It's rational.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Use proof by contradiction.

ghazi
 2 years ago
Best ResponseYou've already chosen the best response.1i 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

ghazi
 2 years ago
Best ResponseYou've already chosen the best response.1you need to use calculator

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1This is obviously rational.

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Right. Still rational though.

ghazi
 2 years ago
Best ResponseYou've already chosen the best response.1there is a fallacy as far as i can see in your solution that you have missed square root on the exponent @djdo525

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0ok guys one correction, that root 2 power root 2 is rational . Sorry But prove that root 2 power root 2 is transcendental

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0Also, PLEASE check whether it is transcendental or not , I am not sure. But I need your help.

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0OK friends I am totally confused. http://www.math.hmc.edu/funfacts/ffiles/30002.35.shtml Here I got that root 2 power root 2 is irrational..

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0^ and as well as transcendental

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.1@Dido525 , your example is incorrect, you showed (sqrt2)^(sqrt2)^sqrt2 is rational but sqrt2^sqrt2 is irrational

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah. That's what he wanted.
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