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Math Help - Rationalizing

  1. #1
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    Unhappy Rationalizing

    I am not sure if I took down the correct notes but...

    In rationalizing denominators, we multiply the denominator on both the top and bottom as such

    \frac{9}{\sqrt{2+7}}X \frac{(\sqrt{2-7})}{(\sqrt{2-7})}<br />

    = \frac{9(\sqrt{2-7})}{(\sqrt{4-7})(\sqrt{2-7})(\sqrt{2-49})}

    \frac{9(\sqrt{2-7})}{-47} in order to get rid of the negative we multiply by (-1) and get \frac{-9(\sqrt{2-7})}{47}

    again did I write my notes in the wrong way?!

    The problem I'm trying to work out is \frac{\sqrt{6}}{\sqrt{5+9}}

    Thanks
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  2. #2
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    Hello, Morzilla!

    Your work makes no sense . . .

    Then at the end you add:

    . . The problem I'm trying to work out is: . {\color{blue}\frac{\sqrt{6}}{\sqrt{5+9}}}


    If that's true, we have: . \frac{\sqrt{6}}{\sqrt{14}} \:=\:\sqrt{\frac{6}{14}} \:=\:\sqrt{\frac{3}{7}} \:=\:\sqrt{\frac{3}{7}\cdot\frac{7}{7}} \:=\:\sqrt{\frac{21}{49}} \:=\:\frac{\sqrt{21}}{\sqrt{49}} \:=\:\frac{\sqrt{21}}{7}


    Why are you messing around with conjugates?

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, Morzilla!

    Your work makes no sense . . .

    Then at the end you add:

    . . The problem I'm trying to work out is: . {\color{blue}\frac{\sqrt{6}}{\sqrt{5+9}}}


    If that's true, we have: . \frac{\sqrt{6}}{\sqrt{14}} \:=\:\sqrt{\frac{6}{14}} \:=\:\sqrt{\frac{3}{7}} \:=\:\sqrt{\frac{3}{7}\cdot\frac{7}{7}} \:=\:\sqrt{\frac{21}{49}} \:=\:\frac{\sqrt{21}}{\sqrt{49}} \:=\:\frac{\sqrt{21}}{7}




    Why are you messing around with conjugates?



    ........cuz, I'm a dummy !

    ....(O.x) ok wait, the answer shown is \frac{\sqrt{30}-9\sqrt{6}}{-76}.....I must admit that I am now 100% lost! Sorry for that.......
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  4. #4
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    Hello, Morzilla!

    Okay, I think I get the idea.
    It would help if you copied the problem correctly.

    And I don't like the way they left their answer . . . very childish!


    Rationalize: . \frac{\sqrt{6}}{\sqrt{5} + 9}
    Rationalize . . . multiply top and bottom by the conjugate . . .

    \frac{\sqrt{6}}{\sqrt{5} + 9}\cdot\frac{\sqrt{5} - 9}{\sqrt{5} - 9} \;=\;\frac{\sqrt{6}(\sqrt{5} - 9)}{(\sqrt{5})^2 - 9^2} \;=\;\frac{\sqrt{6}\!\cdot\!\sqrt{5} - \sqrt{6}\!\cdot\!9}{5 - 81} \;=\;\frac{\sqrt{30} - 9\sqrt{6}}{-76}


    Multiply by \frac{-1}{-1}\!:\;\;\frac{-1(\sqrt{30} - 9\sqrt{6})}{-1(-76)} \;=\;\boxed{\frac{9\sqrt{6} - \sqrt{30}}{76}}


    I don't know anyone past the age of puberty who leaves a negative denomiantor.
    .
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  5. #5
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    Quote Originally Posted by Soroban View Post
    Hello, Morzilla!

    Okay, I think I get the idea.
    It would help if you copied the problem correctly.

    And I don't like the way they left their answer . . . very childish!


    Rationalize . . . multiply top and bottom by the conjugate . . .

    \frac{\sqrt{6}}{\sqrt{5} + 9}\cdot\frac{\sqrt{5} - 9}{\sqrt{5} - 9} \;=\;\frac{\sqrt{6}(\sqrt{5} - 9)}{(\sqrt{5})^2 - 9^2} \;=\;\frac{\sqrt{6}\!\cdot\!\sqrt{5} - \sqrt{6}\!\cdot\!9}{5 - 81} \;=\;\frac{\sqrt{30} - 9\sqrt{6}}{-76}


    Multiply by \frac{-1}{-1}\!:\;\;\frac{-1(\sqrt{30} - 9\sqrt{6})}{-1(-76)} \;=\;\boxed{\frac{9\sqrt{6} - \sqrt{30}}{76}}


    I don't know anyone past the age of puberty who leaves a negative denomiantor.
    .

    So I did write the wrong notes, what a dingus I am!!!

    Thank you so much for all the help!......yeah I never met them either, i just see his ugly ass every morning in the mirror !!

    Well Tomorrow shall be the day.....Again thanks for everything and Happy Festivous!!!
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