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Math Help - Surds

  1. #1
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    Surds

    I have been given a question to expand and simplify this: (3+root6)(2-root3)

    i managed to get it down to 6-3root3-3root2+2root6 but i cannot get it any further, help would be much appreciated.

    PS sorry i could find a square root sign.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by gustifo View Post
    I have been given a question to expand and simplify this: (3+root6)(2-root3)

    i managed to get it down to 6-3root3-3root2+2root6 but i cannot get it any further, help would be much appreciated.

    PS sorry i could find a square root sign.
    Hello gustifo,

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

    I think you simplified it as much as you can.
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  3. #3
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    Hello, gustifo!

    Ya done good!


    Simplify: . (3 + \sqrt{6})(2-\sqrt{3})

    (3+\sqrt{6})(2 - \sqrt{3}) \;=\;(3)(2) + (3)(\text{-}\sqrt{3}) + (\sqrt{6})(2) + (\sqrt{6})(\text{-}\sqrt{3})

    . . = \;6 - 3\sqrt{3} - 2\sqrt{6} - \sqrt{18}


    But \sqrt{18} \:=\:\sqrt{(9)(2)} \:=\:\sqrt{9}\,\sqrt{2} \:=\:3\sqrt{2}


    . . Therefore: . 6 - 3\sqrt{3} - 2\sqrt{6} - 3\sqrt{2}


    And that's as far as we can go . . .


    Edit: Too slow again . . . *sigh*
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