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April 19th, 2019, 10:30 AM   #1
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Radicals and absolute value

Hey. We all know that sqrt (x^2) = |x|. But what about sqrt(x^4), x^(2/4) and so.. are we required to use absolute values here? And why?
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April 19th, 2019, 01:03 PM   #2
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Use of absolute value is a convention, not a mathematical truism. It is used when the context requires one positive number.
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April 19th, 2019, 01:33 PM   #3
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It is seen that $\displaystyle |x^{2} | = x^2 $.
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April 19th, 2019, 08:14 PM   #4
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Quote:
Originally Posted by mathman View Post
Use of absolute value is a convention, not a mathematical truism. It is used when the context requires one positive number.
Didn't get your last statement, could you elaborate more please?
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Originally Posted by idontknow View Post
It is seen that $\displaystyle |x^{2} | = x^2 $.
You mean sqrt(x^4)?

Last edited by Pasta; April 19th, 2019 at 08:16 PM.
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April 20th, 2019, 03:41 AM   #5
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Sqrt(x^2)=|x| .
Sqrt(x^4)=|x^2|=x^2 , x^2 is non-negative.
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April 20th, 2019, 07:24 AM   #6
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Sqrt(x^2)=|x| .
Sqrt(x^4)=|x^2|=x^2 , x^2 is non-negative.
I think I got the idea, so whenever the root and the power of the variable inside are even, and if the resulted power is odd, we add abs value, otherwise we don't right?

Last edited by skipjack; April 20th, 2019 at 06:27 PM.
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April 20th, 2019, 01:22 PM   #7
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Quote:
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Didn't get your last statement, could you elaborate more please?
Example: $\sqrt{x^2}=x$ or $=-x$. For many situations, the needed answer is $|x|$, ignoring the other solution.
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April 20th, 2019, 02:29 PM   #8
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Example: $\sqrt{x^2}=x$ or $=-x$.
Jeez man that's flat out false.
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April 20th, 2019, 06:07 PM   #9
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It's true if $x$ is negative.
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April 20th, 2019, 07:09 PM   #10
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Example: $\sqrt{x^2}=x$ or $=-x$. For many situations, the needed answer is $|x|$, ignoring the other solution.
Right, thanks, and same applies to the other situations i mentioned right? (even power with even root if the result is an odd power)

No he's right @Maschke
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