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Math Help - surds

  1. #1
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    surds

    Express \sqrt{59-24\sqrt{6}} in the form of p\sqrt{2}+q\sqrt{3} , where p and q are integers


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  2. #2
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    Quote Originally Posted by thereddevils View Post
    Express \sqrt{59-24\sqrt{6}} in the form of p\sqrt{2}+q\sqrt{3} , where p and q are integers


    Thanks .
    \sqrt{59-24\sqrt{6}} = p\sqrt{2}+q\sqrt{3}

    Square both sides:

    59 - 24 \sqrt{6} = 2p^2 + 3q^2 + 2pq \sqrt{6}.

    Therefore:

    59 = 2p^2 + 3q^2 .... (1)

    -24 = 2pq \Rightarrow -12 = pq .... (2)

    Solve equations (1) and (2) simultaneously.
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