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mathslover

  • 3 years ago

prove that root 2 power root 2 is irrational .

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  1. Dido525
    • 3 years ago
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    |dw:1358647793062:dw|

  2. mathslover
    • 3 years ago
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    yep

  3. Dido525
    • 3 years ago
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    Well since root 2 is irrational, an irrational number raised to an irrational number should still be irrational.

  4. Dido525
    • 3 years ago
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    But that's not always true. Hmm... Intresting. One moment.

  5. Dido525
    • 3 years ago
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    Thing is, this is NOT an irrational number. It's rational.

  6. Dido525
    • 3 years ago
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    Use proof by contradiction.

  7. Dido525
    • 3 years ago
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    Assume is IS rational.

  8. mathslover
    • 3 years ago
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    ok go on

  9. ghazi
    • 3 years ago
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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

  10. Dido525
    • 3 years ago
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    |dw:1358648074024:dw|

  11. ghazi
    • 3 years ago
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    you need to use calculator

  12. Dido525
    • 3 years ago
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    |dw:1358648102171:dw|

  13. Dido525
    • 3 years ago
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    |dw:1358648120754:dw|

  14. Dido525
    • 3 years ago
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    This is obviously rational.

  15. mathslover
    • 3 years ago
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    ^ two.. not 4

  16. Dido525
    • 3 years ago
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    Right. Still rational though.

  17. ghazi
    • 3 years ago
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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

  18. ghazi
    • 3 years ago
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    sorry its Dido

  19. mathslover
    • 3 years ago
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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

  20. mathslover
    • 3 years ago
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    Also, PLEASE check whether it is transcendental or not , I am not sure. But I need your help.

  21. ghazi
    • 3 years ago
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    lol that was horrible

  22. mathslover
    • 3 years ago
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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..

  23. mathslover
    • 3 years ago
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    ^ and as well as transcendental

  24. dumbcow
    • 3 years ago
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    @Dido525 , your example is incorrect, you showed (sqrt2)^(sqrt2)^sqrt2 is rational but sqrt2^sqrt2 is irrational

  25. mathslover
    • 3 years ago
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    yep

  26. Dido525
    • 3 years ago
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    Yeah. That's what he wanted.

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