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Math Help - surds

  1. #1
    Member GAdams's Avatar
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    surds

    Can't fathom this one:

    Express in the form a + b(root c)

    (root 3 + root 2) (root 3 - root 2)

    Thanks!
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  2. #2
    MHF Contributor
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    Quote Originally Posted by GAdams View Post
    Can't fathom this one:

    Express in the form a + b(root c)

    (root 3 + root 2) (root 3 - root 2)

    Thanks!
    HI

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

    so when you express this in that form ..

    a=1 , b and c are both 0 .
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  3. #3
    Member GAdams's Avatar
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    Quote Originally Posted by mathaddict View Post
    HI

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

    so when you express this in that form ..

    a=1 , b and c are both 0 .
    I get the 1, but thought the question was looking for integer values for b and c other than 0...because if b and c are 0, then you can't actually express as a + b root c?
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  4. #4
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by GAdams View Post
    I get the 1, but thought the question was looking for integer values for b and c other than 0...because if b and c are 0, then you can't actually express as a + b root c?
    They can be zeroes, it still gives a real solution. The original question is multiplying a surd by it's conjugate which will always give a rational answer - it's how we rationalise the denominator.

    You could say that 1 = 1+3\sqrt0

    As long as bc = 0 and c \geq 0 then it will work
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