anonymous
  • anonymous
does the square root of 1, equal 1?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
yes
anonymous
  • anonymous
yes
anonymous
  • anonymous
i feel stupid... thank you :)

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anonymous
  • anonymous
or -1 :)
anonymous
  • anonymous
or^1/2
anonymous
  • anonymous
just 1 period :D
anonymous
  • anonymous
+/- 1 to be correct
anonymous
  • anonymous
actually : \[\sqrt(1) = |1|\] ^_^ and not 1 alone :)
anonymous
  • anonymous
don't feel stupid, alot of ppl missed such simple relation :)
anonymous
  • anonymous
\[\sqrt(x) = |x|\]
nowhereman
  • nowhereman
This is bullpellet. In real analysis the square root is only defined for non-negative numbers. And because it is a function, it can only assume one value for every argument. So the square root of 1 is that non-negative number which squared gives 1, so that is certainly 1. And you don't have to mess around with - or the absolute value function. \[x,y \geq 0 ⇒ \left( \sqrt{x} = y ⇔ y^2 = x\right)\]
anonymous
  • anonymous
>_< nowhereman watch your language lol
anonymous
  • anonymous
are you sure?
anonymous
  • anonymous
actually , that's what my prof said though, and I was shocked LOL
anonymous
  • anonymous
\[1 = \sqrt(1) = \sqrt(1)^2 = \sqrt(-1)^2 = ((-1))^{1/2} = |-1| = 1\] ._. maybe I have misunderstood him?
anonymous
  • anonymous
lol...wait a mind...I think I got you now ^_^"
anonymous
  • anonymous
min*
nowhereman
  • nowhereman
Yes, I'm absolutely sure. ( Only in complex analysis you can describe the square-root function as a riemannian surface with multiple value)
anonymous
  • anonymous
lol wut
nowhereman
  • nowhereman
And of course that definition leads to \[\sqrt{x^2} = |x|\]
nowhereman
  • nowhereman
spaceknight: what are you laughing about?
anonymous
  • anonymous
because i dont understand what you are talking about lol
anonymous
  • anonymous
I understood, thank you nowhereman ^_^
anonymous
  • anonymous
still studying DM :)
anonymous
  • anonymous
are you talking about the principal square root discussed in here http://mathworld.wolfram.com/PrincipalSquareRoot.html because it clearly states For example, the principal square root of 9 is 3, although both and 3 are square roots of 9.
nowhereman
  • nowhereman
Yes, if you want to name it this way. In real analysis, if you are talking about _the_ square root, you mean the principal square root. Of course it is clear that the equation y^2 = x can have 0, 1 or 2 solutions.
anonymous
  • anonymous
Oh, this site is beautiful~ thank you spaceknight! ^_^
anonymous
  • anonymous
but not too much info though , still :)
anonymous
  • anonymous
why does it matter if you are talking about the principal square root or not? everytime i've had to sqrt anything in equations or whatever I've always been told to include the +/-.

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