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Thread: Powers and roots

  1. October 8th 2008, 03:50 PM #1
    Ting
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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 04:02 PM.
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  2. October 9th 2008, 12:31 PM #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. October 9th 2008, 12:37 PM #3
    Jhevon
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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. October 9th 2008, 12:58 PM #4
    Ting
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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. October 9th 2008, 01:04 PM #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. October 9th 2008, 01:13 PM #6
    Jhevon
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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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