mathslover
  • mathslover
prove that root 2 power root 2 is irrational .
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
|dw:1358647793062:dw|
mathslover
  • mathslover
yep
anonymous
  • anonymous
Well since root 2 is irrational, an irrational number raised to an irrational number should still be irrational.

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More answers

anonymous
  • anonymous
But that's not always true. Hmm... Intresting. One moment.
anonymous
  • anonymous
Thing is, this is NOT an irrational number. It's rational.
anonymous
  • anonymous
Use proof by contradiction.
anonymous
  • anonymous
Assume is IS rational.
mathslover
  • mathslover
ok go on
ghazi
  • ghazi
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
anonymous
  • anonymous
|dw:1358648074024:dw|
ghazi
  • ghazi
you need to use calculator
anonymous
  • anonymous
|dw:1358648102171:dw|
anonymous
  • anonymous
|dw:1358648120754:dw|
anonymous
  • anonymous
This is obviously rational.
mathslover
  • mathslover
^ two.. not 4
anonymous
  • anonymous
Right. Still rational though.
ghazi
  • ghazi
there is a fallacy as far as i can see in your solution that you have missed square root on the exponent @djdo525
ghazi
  • ghazi
sorry its Dido
mathslover
  • mathslover
ok guys one correction, that root 2 power root 2 is rational . Sorry But prove that root 2 power root 2 is transcendental
mathslover
  • mathslover
Also, PLEASE check whether it is transcendental or not , I am not sure. But I need your help.
ghazi
  • ghazi
lol that was horrible
mathslover
  • mathslover
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..
mathslover
  • mathslover
^ and as well as transcendental
dumbcow
  • dumbcow
@Dido525 , your example is incorrect, you showed (sqrt2)^(sqrt2)^sqrt2 is rational but sqrt2^sqrt2 is irrational
mathslover
  • mathslover
yep
anonymous
  • anonymous
Yeah. That's what he wanted.

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