# What about the square root function at 0?

Hello everyone,

I was trying to resolve some mathematicals problems about the limits and the functions, but I still don't understand something at all, and I want to know if you can help me !

The problem is that I never understood the trick with 0 and the square root function :

-We know that we can't divide any number by 0, the result won't make any sense.

-We know that a real number divided by his square root is equal to his square root.

For example : 9/3=3, 3 is the square root of 9

But, what is the solution if the real number is 0 ? How do we deal with 0/0=0 ? Is the square root of 0 possible ?

Note by Julien M
1 year, 10 months ago

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Here is the definition of a square root:

$$x \in \mathbb{R}$$ is the square root of $$A$$ if $$x$$ is non-negative and $$x^2 = A$$

According to this definition, 0 does have a square root. According to yours, it does not. But I think it is better to use a definition where more things are defined.

Staff - 1 year, 10 months ago

So the relation sqrt(x) = x/sqrt(x) is not valid for x=0 I guess

- 1 year, 10 months ago

No, it isn't.

Staff - 1 year, 10 months ago