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Math Help - square root of a square root

  1. #1
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    square root of a square root

    g of g(x) = 1/ sqrt( sqrt( 1 / x+2) +2 )

    which could simpify to

    4throot(x+2)/ sqrt(3) if you combine the bottom into one function.

    What i'm interested in is where the sqrt(3) as a denominator came from, and what happened to the two 1 values, did they cancel out.
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  2. #2
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    Quote Originally Posted by fezz349 View Post
    g of g(x) = 1/ sqrt( sqrt( 1 / x+2) +2 )

    which could simpify to

    4throot(x+2)/ sqrt(3) if you combine the bottom into one function.

    What i'm interested in is where the sqrt(3) as a denominator came from, and what happened to the two 1 values, did they cancel out.
    Where did you get that simplification? What is the point of the problem?
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  3. #3
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    my cousin gave me the simplified answer that he received. I proceeded to then try to solve the probem myself and could not receive the same answer he got. I actually couldn't come up with one at all. If that's the right answer i'm looking for a push in the right direction so I'll understand the thought process that's involved with this kind of question.
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  4. #4
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    \frac{1}{\sqrt{\sqrt{\frac{1}{x+2}+2}}}=\frac{1}{\  sqrt{\sqrt{\frac{2x+5}{x+2}}}}=\frac{1}{\left( \frac{2x+5}{x+2} \right) ^{\frac{1}{4}}}

    Assuming I understood what you typed correctly, this is how I would go about starting to simplify this. You have g(g(x)) though. Are you supposed to find g(x)?
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  5. #5
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    no sir, the + 2 is not included on the inner square root, it's by itself under the bigger one. I put the correct equation into the correct equation without a doubt, it's just simplifying it.
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  6. #6
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    Quote Originally Posted by fezz349 View Post
    no sir, the + 2 is not included on the inner square root, it's by itself under the bigger one. I put the correct equation into the correct equation without a doubt, it's just simplifying it.
    Ok, my mistake.

    So it's \frac{1}{\sqrt{\sqrt{\frac{1}{x+2}}+2}}

    This is equal to \frac{1}{\sqrt{\frac{1}{\sqrt{x+2}}+2}}=\frac{1}{\  sqrt{\frac{2\sqrt{x+2}+1}{\sqrt{x+2}}}}

    Now apply the square root separately to the numerator and denominator and keep simplifying. That's the way I'd go about it.
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  7. #7
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    gah... sorry to be a nuisance but i'm not even following how you got to where you did. here's wat my cousin did, and tell me if it makes sense at all to you as well if you don't mind..
    Attached Thumbnails Attached Thumbnails square root of a square root-math.jpg  
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