## anonymous 5 years ago does the square root of 1, equal 1?

1. anonymous

yes

2. anonymous

yes

3. anonymous

i feel stupid... thank you :)

4. anonymous

or -1 :)

5. anonymous

or^1/2

6. anonymous

just 1 period :D

7. anonymous

+/- 1 to be correct

8. anonymous

actually : $\sqrt(1) = |1|$ ^_^ and not 1 alone :)

9. anonymous

don't feel stupid, alot of ppl missed such simple relation :)

10. anonymous

$\sqrt(x) = |x|$

11. 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. $x,y \geq 0 ⇒ \left( \sqrt{x} = y ⇔ y^2 = x\right)$

12. anonymous

>_< nowhereman watch your language lol

13. anonymous

are you sure?

14. anonymous

actually , that's what my prof said though, and I was shocked LOL

15. anonymous

$1 = \sqrt(1) = \sqrt(1)^2 = \sqrt(-1)^2 = ((-1))^{1/2} = |-1| = 1$ ._. maybe I have misunderstood him?

16. anonymous

lol...wait a mind...I think I got you now ^_^"

17. anonymous

min*

18. nowhereman

Yes, I'm absolutely sure. ( Only in complex analysis you can describe the square-root function as a riemannian surface with multiple value)

19. anonymous

lol wut

20. nowhereman

And of course that definition leads to $\sqrt{x^2} = |x|$

21. nowhereman

spaceknight: what are you laughing about?

22. anonymous

because i dont understand what you are talking about lol

23. anonymous

I understood, thank you nowhereman ^_^

24. anonymous

still studying DM :)

25. 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.

26. 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.

27. anonymous

Oh, this site is beautiful~ thank you spaceknight! ^_^

28. anonymous

but not too much info though , still :)

29. 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 +/-.