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: 6,755 Thanks: 695 
Use of absolute value is a convention, not a mathematical truism. It is used when the context requires one positive number.

April 19th, 2019, 01:33 PM  #3 
Senior Member Joined: Dec 2015 From: somewhere Posts: 510 Thanks: 79 
It is seen that $\displaystyle x^{2}  = x^2 $.

April 19th, 2019, 08:14 PM  #4  
Newbie Joined: Apr 2019 From: Jor Posts: 5 Thanks: 0  Quote:
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: 510 Thanks: 79 
Sqrt(x^2)=x . Sqrt(x^4)=x^2=x^2 , x^2 is nonnegative. 
April 20th, 2019, 07:24 AM  #6 
Newbie Joined: Apr 2019 From: Jor Posts: 5 Thanks: 0  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 
Global Moderator Joined: May 2007 Posts: 6,755 Thanks: 695  
April 20th, 2019, 02:29 PM  #8 
Senior Member Joined: Aug 2012 Posts: 2,306 Thanks: 706  
April 20th, 2019, 06:07 PM  #9 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,934 Thanks: 1128 Math Focus: Elementary mathematics and beyond 
It's true if $x$ is negative.

April 20th, 2019, 07:09 PM  #10  
Newbie Joined: Apr 2019 From: Jor Posts: 5 Thanks: 0  Quote:
No he's right @Maschke  

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absolute, radicals, radicsls 
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