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 Pre-Calculus Pre-Calculus Math Forum

 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: 6,821 Thanks: 722 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: 634 Thanks: 91 It is seen that $\displaystyle |x^{2} | = x^2$. April 19th, 2019, 08:14 PM   #4
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 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.
Didn't get your last statement, could you elaborate more please?
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: 634 Thanks: 91 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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 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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 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: 7,963 Thanks: 1148 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 Tags absolute, radicals, radicsls Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post corleoneee Calculus 5 October 22nd, 2013 12:31 AM shiseonji Algebra 2 September 24th, 2013 08:36 AM ohaider Algebra 6 February 6th, 2012 07:13 PM jonquil Algebra 6 April 13th, 2011 03:40 PM Mr_Quick Algebra 3 May 14th, 2009 07:50 AM

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