Absolute Value of "x" versus "x" ?

if I have the fourth root of x^4, why is the answer |x| and not just x?

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  • 9 years ago
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    x^4 is always positive, and the fourth root of Y is always positive (for positive Y). Therefore the fourth root of x^4 is positive.

    So you know you must be looking for a positive number, which means you might imagine |x| could help.

    Remember that x^4 = (-x)^4. Note that if x is negative, then -x is positive, so -x=|x| and thus x^4 = |x|^4. Then you can take that root; this ensures you get a positive number.

    (and of course if x is positive then x=|x| so no worries)

    Hope that helps.

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