Absolute Value of "x" versus "x" ?

Question

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

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thank you!!

Answer 1

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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.