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Math Help - Basic Square Root Help

  1. #1
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    Basic Square Root Help

    How can I solve for z? 3+sqrt(z-6)=sqrt(z+9)
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Basic Square Root Help

    Quote Originally Posted by Espionage View Post
    How can I solve for z? 3+sqrt(z-6)=sqrt(z+9)
    This is going to be a problem in two steps. The base example here is how to solve the following for z:
    \sqrt{z + 1} + 2 = 3

    The general rule is to isolate the square root, then square both sides. In your problem we need to do this twice.

    So
    3 + \sqrt{z-6} = \sqrt{z+9}

    One square root is already isolated, so square both sides:
    9 + 6 \sqrt{z - 6} + (z - 6) = z + 9

    Now isolate the square root:
    6 \sqrt{z - 6} = 6

    And square both sides.

    Always always always when you get a final answer for z make sure it is a solution to the original equation. Extra solutions tend to come out that don't satisfy the original equation.

    -Dan
    Last edited by topsquark; January 8th 2013 at 05:33 PM.
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  3. #3
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    Re: Basic Square Root Help

    Where does the 6 come from when you square both sides the first time?
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  4. #4
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    Re: Basic Square Root Help

    (3 + \sqrt{z - 6})^3 = 3^2 + (2)(3)(\sqrt{z - 6}) + (\sqrt{z - 6})^2 = 9 + 6\sqrt{z - 6} + (z - 6)

    because:

    (a + b)^2 = (a + b)(a + b) = a(a + b) + b(a + b) = a^2 + ab + ba + b^2 = a^2 + 2ab + b^2
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