Square root of number: concept problem I know that the square root of $9$ is $3$
But somebody told me that 
If $x^2= 9$ we get the solution as $x=\pm3$
I am confused when do we have $\sqrt{9}=\pm3$ and only $3$?
Please help.
 A: Take any positive number. For ease, call it $a$. Then it's square is $a^2$.
If we take $a$ and look on the number line to $-a$, you find that this square is also $a^2$. This is because $(-a)^2=(-1)^2 \cdot a^2 = (-1)\cdot(-1)\cdot a^2=a^2$
This means that square rooting any number can hove two possible values, in this case those two values can either be $a$ or $-a$.
When you come to solving equations (I don't know \ can't tell your current working level) you will see that my example is similar to solving $x^2-a^2=0$.
When solving equation it may given some information about the equation, be able to tell whether you choose the positive root or the negative one.
A: $x^2=9$
$x=\pm\sqrt{9}$ ( We took square root of both sides of the equation)
$x=\pm3$
So if we isolate the part $\sqrt{9}$ it is equal to $3$
A: We start with $x^2=9$, we take square root of both sides and we get $\sqrt{x^2}=\sqrt{9}$ or $|x|=3$. The last equation has two solutions but $\sqrt{9}=3$. There is no confusion about that.
A: We do not "have $\sqrt{9}=\pm3$".
We have only $\sqrt9 = 3.$
The expression $\sqrt9$ can never have the value $-3.$
Never, never, never.
(OK, maybe in some relatively obscure branch of math there is such a notation. But not in the standard real arithmetic people generally learn in high school.)
What can happen is that we are looking for the solutions of $x^2 = 9.$
This equation has solutions for two values of $x.$
One of these solutions is $x = \sqrt9.$
The other solution is $x = -\sqrt9.$
Since $\sqrt9 = 3$ (always!), it follows that
$$ -\sqrt9 = -3,$$
and that's how you get the negative solution of $x^2 = 9.$
Sometimes, someone might write that the solutions of $x^2 = 9$
are $x = \pm\sqrt9,$ and you could further write $\pm\sqrt9 = \pm 3.$
But notice that there are $\pm$ signs on both sides of that equation.
