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Math Help - Roots Problem!

  1. #1
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    Roots Problem!

    You know those times when your doing maths and then for some reason you just CANNOT work out why a particular mathematical situation is that way! Well I just did.

    FOr the life of me I cannot work out why the following happens:

    How come

    \sqrt {x^2+y^2}\not= x + y

    Here is my thinking here.

    <br />
\sqrt {x^2+y^2}<br />
= \sqrt {x^2} + \sqrt {y^2}<br />
= x + y<br />

    Please help me out. Because I just have no idea.
    Last edited by mr fantastic; March 12th 2011 at 11:10 PM. Reason: Title.
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  2. #2
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    What is \displaystyle (x + y)^2 when expanded?
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  3. #3
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    Quote Originally Posted by Astar View Post
    You know those times when your doing maths and then for some reason you just CANNOT work out why a particular mathematical situation is that way! Well I just did.

    FOr the life of me I cannot work out why the following happens:

    How come

    \sqrt {x^2+y^2}\not= x + y

    Here is my thinking here.

    <br />
\sqrt {x^2+y^2}<br />
= \sqrt {x^2} + \sqrt {y^2}<br />
= x + y<br />

    Please help me out. Because I just have no idea.
    So you would have \sqrt{1^2 + 1^2} = 1 + 1 ....??!!
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  4. #4
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    Quote Originally Posted by Prove It View Post
    What is \displaystyle (x + y)^2 when expanded?
    It equals x^2 + 2xy + y^2

    So therefore you can say that:

    x+y = \sqrt{(x+y)^2}

    Then what does \sqrt{x^2+y^2} equal then???
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by Astar View Post
    It equals x^2 + 2xy + y^2

    So therefore you can say that:

    x+y = \sqrt{(x+y)^2}

    Then what does \sqrt{x^2+y^2} equal then???
    There is no general further simplification

    CB
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  6. #6
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    Quote Originally Posted by Astar View Post
    ...
    Then what does \sqrt{x^2+y^2} equal then???
    ...

    I think it helps to read \sqrt{x^2+y^2} = (x^2+y^2)^{.5} = (constant)^{.5}

    What you want to do,

    <br />
\sqrt {x^2+y^2}<br />
= \sqrt {x^2} + \sqrt {y^2}<br />
= x + y<br />

    Would be almost correct if it was \sqrt {x^2*y^2} instead of \sqrt {x^2+y^2}.
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