# Thread: Brain fart on square roots

1. ## Brain fart on square roots

√9 = 3
but is it also - 3?

how do i know when a square root is + or -?

2. Originally Posted by NeedHelp18
√9 = 3
but is it also - 3?

how do i know when a square root is + or -?
$\sqrt{9}=3$. I don't think it can be negative. I mean, if it was $-\sqrt{9}$, then it would equal $-3$. But I really don't think it would be negative....i'm not too sure though.

3. Originally Posted by NeedHelp18
√9 = 3
but is it also - 3?

how do i know when a square root is + or -?
Hello,

Indeed, $\sqrt{\dots}$ is always positive (in higher grades it may not, but it's another story )

There is a hesitation to have when you get :

x²=9

Here, x is either 3 either -3. Why ?

x²=9 <=> x²-9=0 <=> (x-3)(x+3)=0

4. Originally Posted by Moo
Hello,

Indeed, $\sqrt{\dots}$ is always positive (in higher grades it may not, but it's another story )

There is a hesitation to have when you get :

x²=9

Here, x is either 3 either -3. Why ?

x²=9 <=> x²-9=0 <=> (x-3)(x+3)=0

Yes, yes indeed!

Then there are imaginary numbers too! like: $\sqrt{-x}=i\sqrt{x}$ ....but who needs to learn that now? ...sorry if i'm confusing you...

5. Originally Posted by Moo
Indeed, $\sqrt{\dots}$ is always positive
$\sqrt 0 = 0$ Are they always positive?

6. Originally Posted by Plato
$\sqrt 0 = 0$ Are they always positive?
Isn't 0 considered as a positive integer ? oO

$0 \in \mathbb{N}$

Erm.. I'm lost

7. Originally Posted by Moo
Isn't 0 considered as a positive integer ?
Absolutely not!
The real numbers are partitioned into three sets: {negatives}, {0}, & {positives}.

Originally Posted by Moo
$0 \in \mathbb{N}$
You are confusing two concepts.
So authors insist that 0 is a counting number.
Some say no it is a whole number but not a natural number.
Others disagree with both of those.
But that has nothing to do with 0 being positive. It is not.

8. Originally Posted by Plato
Absolutely not!
The real numbers are partitioned into three sets: {negatives}, {0}, & {positives}.

You are confusing two concepts.
So authors insist that 0 is a counting number.
Some say no it is a whole number but not a natural number.
Others disagree with both of those.
But that has nothing to do with 0 being positive. It is not.
Oh I see...
In the French wikipedia, it is said that 0 is a natural integer, not in the English one

9. Hi, NeedHelp18!

All positive real numbers have two real square roots. However, the radical notation $\sqrt{a}$ generally refers only to the principal square root, which is always the nonnegative value. If you want to represent both square roots, use the notation $\pm\sqrt{a}$. This also applies to $\sqrt[n]{a},\text{ where }n\text{ is even}$. As others mentioned, things get more complicated when you bring complex values into consideration.

And no, Moo, 0 is neither positive nor negative, but it may be included in the set of natural numbers depending on what definition you are using.