Absolute value and square root

  • #1

Main Question or Discussion Point

what is /squared root sign4x+1 /
what does this equal because i'm confused when it has the square root sign on it all and it's absolute value
 

Answers and Replies

  • #2
cristo
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Do you mean [itex]|\sqrt{4x+1}|[/itex]? Here, the absolute value sign just means take the positive square root.
 
  • #3
yup that's what i mean
 
  • #4
so when i a take the absolute value of it, it looks the same or the square root is gone
 
  • #5
cristo
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The square root is still there, since that is the operation being applied to (4x+1). When we take the square root of a number, we get a positive number, and a negative number (consider the simple example: [itex]\sqrt{4}=\pm 2[/itex], since (-2)2=4=22). By putting the absolute value around the square root is the same as saying that we are taking the positive square root (so, in our example[itex]|\sqrt{4}|=+\sqrt{4}=2[/itex]).

Your expression above can be written [itex]+\sqrt{4x+1}[/itex].
 
  • #6
what happens after i take the absolut value of square root sign4x+1
 
  • #7
so that's what it'll look like
 
  • #8
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Your expression above can be written [itex]+\sqrt{4x+1}[/itex].
Actually, his expression can be written [itex]\sqrt{4x+1}[/itex]. Square roots are defined to be a FUNCTION, which means they CAN'T give you more than one result for any number in their domain (i.e. we can't have [itex]\sqrt{4}=\pm 2[/itex]). By convention, [itex]\sqrt{x} \ge 0[/itex] for all [itex]x \in [0,\infty)[/itex].
 
  • #9
cristo
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Actually, his expression can be written [itex]\sqrt{4x+1}[/itex]. Square roots are defined to be a FUNCTION, which means they CAN'T give you more than one result for any number in their domain (i.e. we can't have [itex]\sqrt{4}=\pm 2[/itex]). By convention, [itex]\sqrt{x} \ge 0[/itex] for all [itex]x \in [0,\infty)[/itex].
Good point; thanks for spotting that, Moo!
 
  • #10
HallsofIvy
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Lets be clear that in general |f(x)| can't be written as simply +f(x)! Here that was true because [itex]\sqrt{x}[/itex] is by definition non-negative. If f(x)= x and x= -4 then |f(x)|= |-4|= 4 while +f(x)= +(-4)= -4.
 

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