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mathslover Group Title

prove that root 2 power root 2 is irrational .

  • one year ago
  • one year ago

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  1. Dido525 Group Title
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    |dw:1358647793062:dw|

    • one year ago
  2. mathslover Group Title
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    yep

    • one year ago
  3. Dido525 Group Title
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    Well since root 2 is irrational, an irrational number raised to an irrational number should still be irrational.

    • one year ago
  4. Dido525 Group Title
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    But that's not always true. Hmm... Intresting. One moment.

    • one year ago
  5. Dido525 Group Title
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    Thing is, this is NOT an irrational number. It's rational.

    • one year ago
  6. Dido525 Group Title
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    Use proof by contradiction.

    • one year ago
  7. Dido525 Group Title
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    Assume is IS rational.

    • one year ago
  8. mathslover Group Title
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    ok go on

    • one year ago
  9. ghazi Group Title
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    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

    • one year ago
  10. Dido525 Group Title
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    |dw:1358648074024:dw|

    • one year ago
  11. ghazi Group Title
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    you need to use calculator

    • one year ago
  12. Dido525 Group Title
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    |dw:1358648102171:dw|

    • one year ago
  13. Dido525 Group Title
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    |dw:1358648120754:dw|

    • one year ago
  14. Dido525 Group Title
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    This is obviously rational.

    • one year ago
  15. mathslover Group Title
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    ^ two.. not 4

    • one year ago
  16. Dido525 Group Title
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    Right. Still rational though.

    • one year ago
  17. ghazi Group Title
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    there is a fallacy as far as i can see in your solution that you have missed square root on the exponent @djdo525

    • one year ago
  18. ghazi Group Title
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    sorry its Dido

    • one year ago
  19. mathslover Group Title
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    ok guys one correction, that root 2 power root 2 is rational . Sorry But prove that root 2 power root 2 is transcendental

    • one year ago
  20. mathslover Group Title
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    Also, PLEASE check whether it is transcendental or not , I am not sure. But I need your help.

    • one year ago
  21. ghazi Group Title
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    lol that was horrible

    • one year ago
  22. mathslover Group Title
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    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..

    • one year ago
  23. mathslover Group Title
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    ^ and as well as transcendental

    • one year ago
  24. dumbcow Group Title
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    @Dido525 , your example is incorrect, you showed (sqrt2)^(sqrt2)^sqrt2 is rational but sqrt2^sqrt2 is irrational

    • one year ago
  25. mathslover Group Title
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    yep

    • one year ago
  26. Dido525 Group Title
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    Yeah. That's what he wanted.

    • one year ago
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