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Math Help - Simplifying surds and fractions

  1. #1
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    Simplifying surds and fractions

    Hi guys,

    How would one simplify the following?


    (2^n x 4^n+1) / 8^n-2


    Also, if x = (√3) + 1 what is the value of x^2 - 1/x^2 with the answer as a simplified surd?
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  2. #2
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    Re: Simplifying surds and fractions

    Quote Originally Posted by Coshy View Post
    (2^n x 4^n+1) / 8^n-2
    Please use * to represent multiplication; x could be a variable...
    Did you mean:
    2^n * 4^(n+1) / 8^(n-2) ?
    Brackets are VERY important here!
    There is a huge difference between 8^n-2 and 8^(n-2); important that you understand that...
    Thanks from MarkFL
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  3. #3
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    Re: Simplifying surds and fractions

    Do you know your rules of exponents? Also, what did you try in solving this problem. Please add some more parentheses, as your notation is a bit confusing on what is the exponent.
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  4. #4
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    Re: Simplifying surds and fractions

    Quote Originally Posted by Coshy View Post
    Hi guys,

    How would one simplify the following?


    (2^n x 4^n+1) / 8^n-2
    I presume you mean, as wilmer suggested, ((2^n)(4^(n+1))/8^(n-2). You need to know that 4= 2^2 and 8= 2^3 so 4^(n+1)= (2^2)^(n+1)= 2^(2(n+1))= 2^(2n+2) and 8^(n-2)= (2^3)^(n-2)= 2^(3(n-2))= 2^(3n- 6).

    So your problem is ((2^n)(2^(2n+2))/(2^(3n- 6)). Combine those. How many "2"s do you have in the numerator and how many in the denominator?


    Also, if x = (√3) + 1 what is the value of x^2 - 1/x^2 with the answer as a simplified surd?
    You know that (√3+ 1)^2= (√3)^2+ 2(√3)+ 1, don't you? And (√3)^2= 3 so x^2= 2(√3)+ 4. For 1/x^2= 1/(2(√3)+ 4), "rationalize the denominator": multiply both numerator and denominator by 2(√3)- 4.

    (This is the third problem you have posted not showing any attempt to do them yourself. I you honestly have no idea how to even begin any of the exercises you are being given, perhaps this course is too difficult for you.)
    Last edited by HallsofIvy; August 8th 2013 at 06:41 AM.
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