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Math Help - [SOLVED] Rationalising Denominators.

  1. #1
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    [SOLVED] Rationalising Denominators.

    Okay, so this is the question...

    (2+√3) / (1+√2)

    This is what I have so far.

    (2+√3) (1-√2) / (1+√2) (1-√2)

    = 2 - 2√2 + √3 - √3√2
    1 - √2 + √2 - √2√2

    Not sure where to go from here?

    Thanks.

    Edit: Sorry, the question on my worksheet is, "Rationalise the denominators of the following..."
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  2. #2
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    Re :

    Quote Originally Posted by Halo View Post
    Okay, so this is the question...

    (2+√3) / (1+√2)

    This is what I have so far.

    (2+√3) (1-√2) / (1+√2) (1-√2)

    = 2 - 2√2 + √3 - √3√2
    1 - √2 + √2 - √2√2

    Not sure where to go from here?

    Thanks.

    Edit: Sorry, the question on my worksheet is, "Rationalise the denominators of the following..."
     \frac{2+\sqrt{3}}{1+\sqrt{2}}\times\frac{1-\sqrt{2}}{1-\sqrt{2}}

    -(2+\sqrt{3})(1-\sqrt{2})
    Last edited by Jhevon; February 1st 2009 at 12:40 PM. Reason: fixed a slight error
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  3. #3
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    Quote Originally Posted by Halo View Post
    Okay, so this is the question...

    (2+√3) / (1+√2)

    This is what I have so far.

    (2+√3) (1-√2) / (1+√2) (1-√2)

    = 2 - 2√2 + √3 - √3√2
    1 - √2 + √2 - √2√2


    after that step try to simplify the problem
    2 - 2√2 + √3 - √3√2
    1 - √2 + √2 - √2√2




    then the answer will be
    2 -2√2 + √3 - √6
    -1

    or



    -(2-2\sqrt{2}+\sqrt{3}-\sqrt{6})
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  4. #4
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    Re :

    Thanks Jhevon , my mistake .
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  5. #5
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    Where did you get the minus sign from?

    Princess could you please explain the second option for your answer?
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  6. #6
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    Quote Originally Posted by Bruce View Post
    Where did you get the minus sign from?

    Princess could you please explain the second option for your answer?


    \frac{2+\sqrt{3}}{1+\sqrt{2}}

    then i rationalized it by multiplying (1-\sqrt{2})

    \frac{2+\sqrt{3}}{1+\sqrt{2}} X \frac{1+\sqrt{2}}{1+\sqrt{2}}

    \frac{2-2\sqrt{2}+\sqrt{3}-\sqrt{6}}{1-\sqrt{2}+\sqrt{2}-\sqrt{2}\sqrt{2}}

    \frac{2-\sqrt{2}+\sqrt{3}+\sqrt{6}}{1-4}

    \frac{2-\sqrt{2}+\sqrt{3}+\sqrt{6}}{-1}

    -(2-\sqrt{2}+\sqrt{3}+\sqrt{6})]

    -(2+\sqrt{3})(1-\sqrt{2})

    i have the same answer as Jhevon i just simplified it by multiplying.
    Last edited by princess_21; February 3rd 2009 at 04:38 AM.
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