My Math Forum Radicals and absolute value

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 April 19th, 2019, 10:30 AM #1 Newbie   Joined: Apr 2019 From: Jor Posts: 5 Thanks: 0 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?
 April 19th, 2019, 01:03 PM #2 Global Moderator   Joined: May 2007 Posts: 6,807 Thanks: 717 Use of absolute value is a convention, not a mathematical truism. It is used when the context requires one positive number. Thanks from idontknow
 April 19th, 2019, 01:33 PM #3 Senior Member   Joined: Dec 2015 From: somewhere Posts: 605 Thanks: 88 It is seen that $\displaystyle |x^{2} | = x^2$.
April 19th, 2019, 08:14 PM   #4
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Quote:
 Originally Posted by mathman Use of absolute value is a convention, not a mathematical truism. It is used when the context requires one positive number.
Quote:
 Originally Posted by idontknow 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.

 April 20th, 2019, 03:41 AM #5 Senior Member   Joined: Dec 2015 From: somewhere Posts: 605 Thanks: 88 Sqrt(x^2)=|x| . Sqrt(x^4)=|x^2|=x^2 , x^2 is non-negative.
April 20th, 2019, 07:24 AM   #6
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Quote:
 Originally Posted by idontknow 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.

April 20th, 2019, 01:22 PM   #7
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Quote:
 Originally Posted by Pasta 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.

April 20th, 2019, 02:29 PM   #8
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Quote:
 Originally Posted by mathman Example: $\sqrt{x^2}=x$ or $=-x$.
Jeez man that's flat out false.

 April 20th, 2019, 06:07 PM #9 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond It's true if $x$ is negative.
April 20th, 2019, 07:09 PM   #10
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Quote:
 Originally Posted by mathman 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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