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Math Help - Powers and roots

  1. #1
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    Powers and roots

    Hello

    The problem says to insert brackets to make this a true statement

    <br />
\sqrt{2}^{{\sqrt{2}}^{{\sqrt{2}}^{\sqrt{2}}}} = <br />
\sqrt{2}^{{\sqrt{2}}^{\sqrt{2}}}<br />

    I know that:

    <br />
\sqrt{2}^{\sqrt{2}} = 2^{\frac{\sqrt2}{2}}<br />

     <br />
(\sqrt{2}^{\sqrt{2}})^{\sqrt{2}} = 2<br />

    I'm not sure how to proceed from here, apart from brute force. A hint would be appreciated.
    Last edited by Ting; October 8th 2008 at 05:02 PM.
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  2. #2
    Moo
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    Hello !

    Noting that (\sqrt{2}^{\sqrt{2}})^{\sqrt{2}} = 2 is a good thing !

    However, and pardon me for that, but I don't know how I got to the answer... It was quite automatic

    \sqrt{2}^{\left(\left({\sqrt{2}}^{\sqrt{2}}\right)  ^{\sqrt{2}}\right)}=\left(\sqrt{2}^{\sqrt{2}}\righ  t)^{\sqrt{2}}

    (it equals 2)
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Moo View Post
    However, and pardon me for that, but I don't know how I got to the answer... It was quite automatic
    i see, your genius is a mystery--even to you!
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  4. #4
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    Dear Moo

    Thank you!

    Guess I'll just have to work on developing the kind of automatic response you have.

    Ting
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  5. #5
    Moo
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    Quote Originally Posted by Jhevon View Post
    i see, your genius is a mystery--even to you!
    Lol am I able not to agree ?
    Quote Originally Posted by Ting View Post
    Dear Moo

    Thank you!

    Guess I'll just have to work on developing the kind of automatic response you have.

    Ting
    You're welcome !
    Actually, I think that at first I was telling myself that the RHS needed parentheses. Making parentheses over the last 2 sqrt(2) wouldn't have made the problem easier. So if there were, it should have been over the first two sqrt(2)

    After that...blackout...
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Moo View Post
    Lol am I able not to agree ?
    no

    ... After that...blackout...
    yup, she turned into the super math-solving Hulk.
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