Is a number written in the square root/fraction form called a non-integer even if it can be simplified to an integer This is very simple question, but I cannot get the ansewer from the internet.

Is a number written in the square root/fraction form called a non-integer even if it can be simplified to an integer. 

For example 4/2, 12/4, sqr4, sqr64 etc... do these need to be simplified before we can call them integers.

Too make this easer to understand are sqr64 and 12/4 non-integers while 8 and 3 are integers.
No.  Numbers are what they are.  It doesn't matter how they are represented. 

$7$ is an integer.  Period.  

It doesn't matter if is written as $5 + 2$ or $\sqrt{49}$ or $\sqrt{25} + \frac{\sqrt[3]{16}}{2^{\frac 13}}$ or $\ln (e^7)$.

Those are all equal to $7$ and $7$ is an integer.  Period.

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That said, it might not be easy (or even possible) to tell if a number is or is not an integer.  It's obvious that $7$ is an integer and $7.0000012142650469991421281354411.....$ isn't.  But it isn't clear whether $\sqrt[7]{823543}$ or $\sqrt[7]{823544}$ are integers.  (It turns out that those are the same numbers.)

But it doesn't matter whether we know if a number is an integer or not.   It either is or isn't.
If it can be simplified to an integer,
it can be called an integer
after the simplification.

Until the simplification is done,
I would just call the expression
"an expression"
when it is not clear if it could be
simplified to an integer.

Considering how expressions
involving nested radicals
can be sometimes
amazingly simplified,
I think that there would be cases
where the fact that
an expression simplifies
to an integer
is a surprise.