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Math Help - How does sqrt(x^2) = 1?

  1. #1
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    How does sqrt(x^2) = 1?

    Hey guys, I just have quick question:

    How does \frac{\sqrt{9x^2+x}}{x} = \sqrt{9+1/x} knowing that \sqrt{x^2} = x

    big thanks.
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  2. #2
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    Assuming that \displaystyle x \geq 0, then \displaystyle \sqrt{x^2} = x.

    Since \displaystyle \frac{\sqrt{9x^2 + x}}{x} = \frac{\sqrt{9x^2 + x}}{\sqrt{x^2}}

    \displaystyle = \sqrt{\frac{9x^2 + x}{x^2}}.

    Go from here.
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  3. #3
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    Thank you! I got it.
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