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Math Help - Rationalising surd/simplifying denominator

  1. #1
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    Rationalising surd/simplifying denominator

    Hello

    I have been struggling terribly with a surd problem to the point that it's beginning to hurt }:-/

    I have: √3
    √2(√6-√3)
    The answer is given as :
    (2+√2)
    2

    I want to multiply the denominator by itself to clear the surds, but end up with a way too complicated answer.
    I realise that

    (√6-√3)(√6+√3) would rationalise part of the problem, but the √2 is really giving me a hard time...Using logic I feel I want to multiply by √2(√6+√3) but can't get anywhere near the answer if I do.

    Cold someone shed some light for me please ?

    Thank you!

    Apologies for formatting, the question and answer are fractions of course*
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Freaked View Post
    Hello

    I have been struggling terribly with a surd problem to the point that it's beginning to hurt }:-/

    I have: √3
    √2(√6-√3)
    The answer is given as :
    (2+√2)
    2

    I want to multiply the denominator by itself to clear the surds, but end up with a way too complicated answer.
    I realise that

    (√6-√3)(√6+√3) would rationalise part of the problem, but the √2 is really giving me a hard time...Using logic I feel I want to multiply by √2(√6+√3) but can't get anywhere near the answer if I do.

    Cold someone shed some light for me please ?

    Thank you!

    Apologies for formatting, the question and answer are fractions of course*
    As you say

    \displaystyle \frac{\sqrt{3}}{\sqrt{2}(\sqrt{6} - \sqrt{3})}


    \displaystyle = \frac{\sqrt{3}}{\sqrt{2}(\sqrt{6} - \sqrt{3})} \cdot \frac{\sqrt{2}(\sqrt{6} + \sqrt{3})}{\sqrt{2}(\sqrt{6} + \sqrt{3})}

    \displaystyle = \frac{\sqrt{3} \cdot \sqrt{2}(\sqrt{6} + \sqrt{3})}{\sqrt{2}(\sqrt{6} - \sqrt{3}) \cdot \sqrt{2}(\sqrt{6} + \sqrt{3})}

    \displaystyle = \frac{ \sqrt{6}(\sqrt{6} + \sqrt{3})}{2(6 - 3)}

    Can you finish from here?

    -Dan
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  3. #3
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    OK

    My problem then is that I couldn't simply see that √2(√6+√3) . √2(√6-√3) is straight forward...I felt that I needed to multiply all the root terms (√6-√3) by √2 as well..I will need to think about that now

    Thanks : )
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