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Math Help - Radicals, Radical functions and rational exponents Help please

  1. #1
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    Wink Anyone that can help please on radical functions?

    The algebraic expression: I am not sure how to type this on the computer but in the parenthesis is the square root of t+h - square root of t over h

    15.92(square root of t + h - square root of t over h)
    models the average rate of change in the percentage of households online from t years after 1997 to t + h years after 1997. Use the expression to solve this problem...

    Let t=4 and h=2. Evaluate the expression to find the average rate of change in percentage of households online from 2001-2003 that is, between 4 years and 4 + 2, or 6 years after 1997.
    Last edited by kbryant05; June 4th 2006 at 07:06 PM. Reason: Not getting a response
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  2. #2
    MHF Contributor Quick's Avatar
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    Is the expression,
     15.92\left(\sqrt{t+h} - \sqrt{\frac{t}{h}} \right)
    or
     15.92\left(\sqrt{t+h} - \frac{\sqrt{t}} {h}\right)
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  3. #3
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    Radical Expression

    I wish I could do what you just did with the numbers but it is everything over h. Does that make sense?
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  4. #4
    MHF Contributor Quick's Avatar
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    \frac{15.92\left(\sqrt{t+h} - \sqrt{t}\right)}{h}
    like this?
    Also, do you need this in simplest radical form or decimal
    Last edited by Quick; June 4th 2006 at 03:54 PM.
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  5. #5
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    Awesome Job

    Yes that is how it is written awesome job. Yes to have in simplest form. I have tried several times to get it to work and can't seem to get it yet to work out.
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  6. #6
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    Not sure if this helps

    I am not sure if this helps at all but my book has a an average rate change of 3.6% but I am not getting it at all? I am lost on this whole radical stuff.
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  7. #7
    MHF Contributor Quick's Avatar
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    \frac{15.92\left(\sqrt{t+h} - \sqrt{t}\right)}{h}
    \frac{15.92}{h}\left(\sqrt{t+h} - \sqrt{t}\right)
    \frac{15.92}{2}\left(\sqrt{4+2} - \sqrt{4}\right)
    7.96\left(\sqrt{6} - \sqrt{4}\right)
    \sqrt{63.3616}\left(\sqrt{6} - \sqrt{4}\right)
    \sqrt{63.3616}\sqrt{6} - \sqrt{63.3616}\sqrt{4}
    \sqrt{63.3616\cdot6} - \sqrt{63.3616\cdot4}
    \sqrt{380.1696} - \sqrt{253.4464}
    \sqrt{96\cdot3.9601} - \sqrt{64\cdot3.9601}
    \sqrt{96}\sqrt{3.9601} - \sqrt{64}\sqrt{3.9601}
    \left(\sqrt{96}-\sqrt{64}\right)\left(\sqrt{3.9601}\right)
    \left(\sqrt{16\cdot6}-8\right)\left(\sqrt{3.9601}\right)
    \left(4\sqrt{6}-8\right)\left(\sqrt{3.9601}\right)

    Considering I'm not even in high school, this is as far as I could get without going insane. Maybe Black or Hacker could get you farther.
    Last edited by Quick; June 4th 2006 at 04:47 PM.
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  8. #8
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    Sorry I messed up

    Oh my goodness I am so sorry I meant when I said everything being over h it was supposed to be the parenthesis only and the 15.92 on the side. I am so very sorry. I feel horrible.
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  9. #9
    MHF Contributor Quick's Avatar
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    That's okay, but is this the real expression?
     15.92\left(\frac{\sqrt{t+h}-\sqrt{t}}{h}\right)
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  10. #10
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    Correct

    I can't express how sorry I am. Thank you for helping me.
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  11. #11
    MHF Contributor Quick's Avatar
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    Actually, it doesn't matter, because all three of these are the same thing.
     \frac{15.92}{h}\left(\sqrt{t+h} - \sqrt{t}\right)

     \frac{15.92\left(\sqrt{t+h} - \sqrt{t}\right)}{h}

     15.92\left(\frac{\sqrt{t+h} - \sqrt{t}}{h}\right)}

    So my answers the same, sorry I couldn't finish helping you.
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  12. #12
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    Thanks Quick

    Thank you for trying. i hope someone else can try to do it too.
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  13. #13
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Quick
    \frac{15.92\left(\sqrt{t+h} - \sqrt{t}\right)}{h}
    \frac{15.92}{h}\left(\sqrt{t+h} - \sqrt{t}\right)
    \frac{15.92}{2}\left(\sqrt{4+2} - \sqrt{4}\right)
    7.96\left(\sqrt{6} - \sqrt{4}\right)
    Considering I'm not even in high school, this is as far as I could get without going insane. Maybe Black or Hacker could get you farther.
    well done, Quick
    just substitute the value of 6^(1/2) and you will get the answer
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  14. #14
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    I don't get it??

    This is what I have tried to do to come up with 3.6% but am off still??

    15.92 (√ t + h -√ t)
    h

    15.92 (√ 4 + 2 - √ 4)
    2
    15.92 (√ 6 - √ 4)
    2
    √ 3.99 √ 6 - √ 3.99 √ 4
    √3.99 * 6 - √ 3.99 * 4
    √23.94 - √15.96 = √7.98/2 = 3.9
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  15. #15
    Super Member malaygoel's Avatar
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    Quote Originally Posted by kbryant05
    This is what I have tried to do to come up with 3.6% but am off still??

    15.92 (√ t + h -√ t)
    h

    15.92 (√ 4 + 2 - √ 4)
    2
    15.92 (√ 6 - √ 4)
    2
    7.96(2.4494 - 2)
    = 7.96 * 0.4494
    =3.577
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