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Math Help - rationalise

  1. #1
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    rationalise

    (5sqrt3) / (sqrt3 - sqrt2)

    i got 15 - 5sqrt2

    but is that right???
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  2. #2
    Senior Member Stroodle's Avatar
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    Hi there.

    The answer is 15+5\sqrt{6} - obtained by multiplying the numerator and the denominator of the fraction by \sqrt{3}+\sqrt{2} - the conjugate of \sqrt{3}-\sqrt{2}
    Last edited by Stroodle; December 3rd 2009 at 12:42 AM. Reason: error
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  3. #3
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by deej813 View Post
    (5sqrt3) / (sqrt3 - sqrt2)

    i got 15 - 5sqrt2

    but is that right???
    \frac{5 \sqrt{3}}{\sqrt{3}-\sqrt{2}}

    \frac{5 \sqrt{3}(\sqrt{3}+\sqrt{2})}{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2})}
    using the property
    (a+b)(a-b) = a^2 - b^2 for denominator
    we get

    \frac{5 \sqrt{3}(\sqrt{3}+\sqrt{2})}{3-2}

    \frac{5*3+5\sqrt{2*3})}{1}

    15+5\sqrt{6}
    I think you messed up in last step
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