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#7 - tazze
Reply +127
(07/12/2013) [-]
actually, it's 2 and -2   
inb4 red thumbs
actually, it's 2 and -2
inb4 red thumbs
#148 to #7 - animedudej
Reply 0
(07/13/2013) [-]
inb4 trip thumbs
#136 to #7 - anon
Reply 0
(07/13/2013) [-]
Nope. This is why notation is critically important.

The radical √n denotes only the principal value. The content only shows the principal root, therefore we should only see positive 2's.
#130 to #7 - usaisnotamerica
Reply 0
(07/13/2013) [-]
But still its =2.
#112 to #7 - anon
Reply 0
(07/13/2013) [-]
That square root sign means only the positive square root. 2 is the right answer.
#75 to #7 - kaxu
Reply 0
(07/13/2013) [-]
Depends if you are on R or on C
#135 to #75 - anon
Reply 0
(07/13/2013) [-]
It depends on whether one considers the principal square root function or the multivalued relation. Choosing between R and C is irrelevant (for what anyway? domain? codomain?). You can map from reals to reals with a real image and still have both the positives and negatives. It just won't be a function. R vs C is irrelevant.
#74 to #7 - rothingham
Reply -1
(07/12/2013) [-]
2 OR -2, not AND, OR.
#60 to #7 - shredheadxd
Reply +1
(07/12/2013) [-]
If you start with 4, then take the square root, then you are right. The answers are 2, and -2.

But if you start with the square root of 4, then you are wrong. The only answer is 2.

Sincerely,
A 4th year math major, not that anybody cares.
#137 to #60 - anon
Reply 0
(07/13/2013) [-]
Not really. In this case, it's not really clear whether or not we're talking about the just the principal value or not. Unlike written out mathematical notation, words can be ambiguous on this matter. So we clarify,

You start with 4, take the (principal) square root, and you will only have 2. Likewise, if you start with the (principal) square root of 4, then you will still only have 2.
#143 to #137 - shredheadxd
Reply +1
(07/13/2013) [-]
On the contrary,
When you do the action of square rooting, you must consider the positive and negative cases. Since you do not know whether the square root was principal or not, you must consider both cases. The positive case is the one shown in the content - the principal square root. The negative case will give you -2.

If you start with simply "square root of 4", you have skipped the action of square rooting, and jump right to evaluating the positive case (the principal square root).

It is quite extremely crystal clear.
#202 to #143 - bronybox
Reply 0
(07/13/2013) [-]
Then would you (should you?) not write in the notation "±√4" as opposed to simply writing the notation for the principal square root?
#204 to #202 - shredheadxd
Reply 0
(07/14/2013) [-]
Lemme break it down.

±√4 = +√4 AND -√4 (it's "AND" or "OR" depending on the situation)
+√4 = √4 = 2
-√4 = -2

So if you just look at the above statements, you can see that √4 = 2. Not -2. Math don't lie!
#205 to #204 - bronybox
Reply 0
(07/14/2013) [-]
Isn't that what I've been saying?
√4 = 2 and only 2
-√4 = -2 and only -2

That's been my point throughout this entire discussion.
#206 to #205 - shredheadxd
Reply 0
(07/15/2013) [-]
that's correct! I wasn't sure what you were talking about, but the math wasn't ambiguous so I just reiterated it.
#207 to #206 - ambiguous **User deleted account**
Reply 0
(07/15/2013) [-]
I stopped looking at porn for this?
I stopped looking at porn for this?
#208 to #207 - shredheadxd
Reply 0
(07/15/2013) [-]
I usually get off to my own comments too!
#100 to #60 - anon
Reply 0
(07/13/2013) [-]
I was going to say this. The difference is subtle, but it's surely there and will affect some problems.
#54 to #7 - mrloverlover
Reply +15
(07/12/2013) [-]
everyone is replying to this with math equations etc.

and i'm just sat here thinking what the **** is wrong with that dog
#53 to #7 - warbob
Reply 0
(07/12/2013) [-]
square root is a function that is always equal or above 0.
mathematically put : sqrt(x) >= 0
#33 to #7 - bronybox
Reply +4
(07/12/2013) [-]
Get ready to learn ************(s).

As displayed by the graph of a square root function (shown on the left), there are no negative y values, and thus f(x) can never be negative [ sqrt(2) can never equal - 2 ]. This is because the square root operation IS A function, and thus their can only be 1 y value for every x value (but not necessarily the other way around).

You are stating one of the most common misconceptions people have once they are taught to solve quadratic equations, observe.

1. x^2 = 4
2. x = sqrt (4)
3. x = ± 2

You make the assumption that the square root of 4 is equal to +/- 2, however, by actual mathematical definition, line 2 holds a mistake. This is because x DOES NOT equal sqrt(4). The correct solution is:

1. x^2 = 4
2. x = ± sqrt(4)
3. x = ± 2

Just as you cannot take the square root of a negative number, the square root of a positive number can never be negative. The radical symbol by definition is only the principal square root, i.e., always positive.
#154 to #33 - kikisu
Reply 0
(07/13/2013) [-]
Wait wait, you're totally wrong. If the square root of a positive number can never be negative, why is -2 squared 4? That one you have up is only the positive, not negative roots.
#169 to #154 - bronybox
Reply -1
(07/13/2013) [-]
You're not understanding the definition of a square root. I even put a graph there and everything.
#195 to #169 - kikisu
Reply 0
(07/13/2013) [-]
I am. If you take the root of 4, its both -2 and 2. But if you already have the square root of four, its just two. I do understand the definition of a square root, with is a number that when multiplied by itself gives you the original. -2 times -2 is 4.
#197 to #195 - bronybox
Reply 0
(07/13/2013) [-]
I'm saying the square root operation signified by the radix will only yield the positive roots of a number by definition.
#198 to #197 - kikisu
Reply 0
(07/13/2013) [-]
If you start with a square root yeah. But if I take a square root it will be both.
#199 to #198 - bronybox
Reply 0
(07/13/2013) [-]
But when you take the square root, you are taking the positive and negative root, and you SHOULD technically be using the notation "±sqrt (a)", otherwise what you are writing is simply incorrect by means of notation. You may be doing the right thing in your head, but you're not writing down what you should be.
#200 to #199 - kikisu
Reply 0
(07/13/2013) [-]
I never said anything about not having the plus or minus sign. But yeah I see what you mean.
#126 to #33 - anon
Reply 0
(07/13/2013) [-]
you sure can take a square root of an imaginary number; you just have to use complex numbers.
[url deleted]
[url deleted]
#128 to #126 - anon
Reply 0
(07/13/2013) [-]
forgot about the stupid url deleting
[url deleted] [url deleted] /wiki/Squar e_root
[url deleted] [url deleted] omplex.htm
#125 to #33 - anon
Reply 0
(07/13/2013) [-]
Math'd. Good job.
#119 to #33 - ningyoaijin
Reply 0
(07/13/2013) [-]
>using a badly coded graphing software to demonstrate an incorrect point
#201 to #119 - bronybox
Reply 0
(07/13/2013) [-]
Type the square root of x into any graphing software and I assure you it will either give you that exact graph (might also include the imaginary part as well, a reflection along the y-axis)

Here's an example from Wolfram|Alpha
#134 to #119 - anon
Reply 0
(07/13/2013) [-]
The only bad part I see is "the square root of a positive number can never be negative". However, given the context one can easily tell that he's still referring to the principal square root.

Besides this, how is he incorrect? (unless this is what you meant)
#59 to #33 - kjelli
Reply 0
(07/12/2013) [-]
why are you thumbed down, this is correct
#23 to #7 - Kelsenial
Reply 0
(07/12/2013) [-]
Good god that's terrifying
#17 to #7 - anon
Reply 0
(07/12/2013) [-]
but thats only if you bring in the square root yourself.
#16 to #7 - drfaust
Reply +1
(07/12/2013) [-]
Actually by definition it's only positive 2. Even though -2 squared is 4, the square root of 4 is 2.
#26 to #16 - deathstare
Reply -2
(07/12/2013) [-]
-2 * -2 = 4
2 * 2 = 4

(sqrt) 4 = +/- 2
#21 to #16 - yunablade
Reply +1
(07/12/2013) [-]
both results are valid, the correct answer is: +/− 2
#29 to #21 - anon
Reply 0
(07/12/2013) [-]
Both x=+2 and x=-2 are solutions to x^2=4. HOWEVER, sqrt(x) is defined as the POSITIVE solution to x^2=4. Hence sqrt(4)=2 and not +/-2.
#30 to #29 - yunablade
Reply -2
(07/12/2013) [-]
Maybe it's a cultural thing, when I took math I was required to express the results to a square root always as +/- (unless imaginary number) and if the root was part of a bigger operation record both results (when the value is negative and when positive)
#144 to #30 - shredheadxd
Reply 0
(07/13/2013) [-]
Don't say these things.
#45 to #30 - kabuthefox
Reply +1
(07/12/2013) [-]
math is "universal"
#14 to #7 - anon
Reply 0
(07/12/2013) [-]
Wut.. square root of 4 is 2, not -2
#24 to #14 - nazrix
Reply -2
(07/12/2013) [-]
x² = 4
√x² = √4
│x│= 2
±x = 2
so,
x = ±2
#36 to #24 - bronybox
Reply -1
(07/12/2013) [-]
You are 100% correct, there are two solutions to x^2 = 4, ±2
HOWEVER.

You are wrong in the fact that √x² = √4
It should be ±√x² = ±√4

Because √x is a function (let's denote it f(x) = √x)
f(x) can never equal both 2 and -2 when x = 4 by the definition of a function.
#192 to #36 - nazrix
Reply 0
(07/13/2013) [-]
ever heard of an injective function?
f(x) = f(y) => x=y

there are, however, functions that are not injective. quite many.
#196 to #192 - bronybox
Reply 0
(07/13/2013) [-]
An injective function is the basic function we always think of, I don't understand what you mean. The square root of x does happen to be an injective function by it's definition.
#191 to #36 - nazrix
0
has deleted their comment [-]
#190 to #36 - nazrix
0
has deleted their comment [-]
#42 to #36 - metaldrone
Reply -1
(07/12/2013) [-]
STOP IT!!! I'm learning.
#37 to #36 - bronybox
Reply -1
(07/12/2013) [-]
Or rather, you aren't wrong that √x² = √4 , it is simply an incomplete statement.
#25 to #24 - pooplol
Reply 0
(07/12/2013) [-]
thats only if you bring in the square root yourself
#20 to #14 - yunablade
Reply 0
(07/12/2013) [-]
You might want to reconsider
You might want to reconsider
#15 to #14 - palewolf
Reply 0
(07/12/2013) [-]
No, he's correct, -2 multiplied by -2 is 4. That's basic maths.