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Thread: Absolute Vaule

  1. #1
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    Absolute Vaule

    1.$\displaystyle \sqrt[4]{8x^5}$

    $\displaystyle 2|x|\sqrt{x}$

    2.$\displaystyle \sqrt{49x^6}$

    $\displaystyle 7|x^3| or |7x^3$|? which one is valid?

    3.$\displaystyle \sqrt{x^3}$

    $\displaystyle |x|\sqrt{x}$?
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  2. #2
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    Re: Absolute Vaule

    How do you use absolute value for radicals?
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    Re: Absolute Vaule

    Hi, are you working in $\displaystyle \mathbb{R}$? If so,
    $\displaystyle |x|\sqrt{x}=x\sqrt{x}$ because the domain of $\displaystyle \sqrt{x}$ is $\displaystyle \mathbb{R}^+\cup{}\left\{0\right\}$
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    Re: Absolute Vaule

    Quote Originally Posted by theloser View Post
    [snip]
    2.$\displaystyle \sqrt{49x^6}$

    $\displaystyle 7|x^3| or |7x^3$|? which one is valid?

    [snip]
    Both. But obviously the first is simpler.

    And you should note that:

    1. the domain of $\displaystyle \sqrt{x^n}$ is $\displaystyle x \geq 0$ if n is odd (why?) and so |x | = x under such circumstances.

    2. the domain of $\displaystyle \sqrt{x^n}$ is $\displaystyle R$ if n is even (why?).
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