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Math Help - Question on Laws of Exponents

  1. #1
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    Question on Laws of Exponents

    Ok I'm at the end of my lesson and I have to prove if an expression is true or false.

    eg: (x+y)^{1/2} = x^{1/2}+y^{1/2}

    I know if it were (xy)^{1/2} this would be equal to x^{1/2}y^{1/2} but the addition sign is throwing me off.

    I've looked at my rules and can't find anything like  (x+y)^2 laws just the power of the product.

    I hope I'm making sense :P

    Thanks
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  2. #2
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    It's not true. You can check using the Binomial Series...
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  3. #3
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    Quote Originally Posted by Substince View Post
    Ok I'm at the end of my lesson and I have to prove if an expression is true or false.

    eg: (x+y)^{1/2} = x^{1/2}+y^{1/2}

    I know if it were (xy)^{1/2} this would be equal to x^{1/2}y^{1/2} but the addition sign is throwing me off.

    I've looked at my rules and can't find anything like  (x+y)^2 laws just the power of the product.

    I hope I'm making sense :P

    Thanks
    1. Re-write the expression as:

    \sqrt{x+y}=\sqrt{x} + \sqrt{y}

    2. Square both sides and you'll see that this equation is only true if x = 0 or y = 0
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  4. #4
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    wonderful thank you guys!
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