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 ?

#Algebra

Easy Math Editor

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Comments

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.

Agnishom Chattopadhyay - 4 years, 9 months ago

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

Julien M - 4 years, 9 months ago

No, it isn't.

Agnishom Chattopadhyay - 4 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$