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Math Help - Surd q?

  1. #1
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    Surd q?

    Rationalise the denominator of 1 + √3 (1 + √3)
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Detanon View Post
    Rationalise the denominator and numerator of 1 + √3 (1 + √3)
    Multiply the denominator by its conjugate.
    Last edited by VonNemo19; December 17th 2009 at 06:04 AM.
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  3. #3
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    How do you find the conjugate?
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Detanon View Post
    How do you find the conjugate?
    Example:

    The conjugate of a+b is a-b.
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  5. #5
    A riddle wrapped in an enigma
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    Quote Originally Posted by Detanon View Post
    Rationalise the denominator of 1 + √3 (1 + √3)
    Hi Detanon,

    The conjugate of a+b\sqrt{r} is a-b\sqrt{r}

    \frac{1+\sqrt{3}}{(1+\sqrt{3})^2}=\frac{1+\sqrt{3}  }{4+2\sqrt{3}}

    Now, multiply numerator and denominator by 4-2\sqrt{3}
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  6. #6
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    I got (1 + 2√3) 2. but in my book it says the answer is (5 + 3√3) 2
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  7. #7
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    Smile

    \frac{1+\sqrt{3}}{(1+\sqrt{3})^2}=\frac{1+\sqrt{3}  }{4+2\sqrt{3}}<br />
\times \frac{4-2\sqrt{3}}{4-2\sqrt{3}}=\frac{4-2\sqrt{3}+4\sqrt{3}-6}{16-12}=\frac{-2+2\sqrt{3}}{4}=\frac{-1+\sqrt{3}}{2}
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