Question

does the square root of 1, equal 1?

Answer 1

yes

Answer 2

yes

Answer 3

i feel stupid...
thank you :)

Answer 4

or -1 :)

Answer 5

or^1/2

Answer 6

just 1 period :D

Answer 7

+/- 1 to be correct

Answer 8

actually :

\[\sqrt(1) = |1|\] ^_^ and not 1 alone :)

Answer 9

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

Answer 10

\[\sqrt(x) = |x|\]

Answer 11

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

Answer 12

>_< nowhereman watch your language lol

Answer 13

are you sure?

Answer 14

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

Answer 15

\[1 = \sqrt(1) = \sqrt(1)^2 = \sqrt(-1)^2 = ((-1))^{1/2} = |-1| = 1\]

._. maybe I have misunderstood him?

Answer 16

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

Answer 17

min*

Answer 18

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

Answer 19

lol wut

Answer 20

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

Answer 21

spaceknight: what are you laughing about?

Answer 22

because i dont understand what you are talking about lol

Answer 23

I understood, thank you nowhereman ^_^

Answer 24

still studying DM :)

Answer 25

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.

Answer 26

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.

Answer 27

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

Answer 28

but not too much info though , still :)

Answer 29

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 +/-.