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I'm not sure how to ask but I hope you will understand.

Let's say we have such root: $$m\sqrt[2] n$$ or $$2\sqrt[2]3$$ So could you please tell me how to call m or 2 and n or 3 and how to say everything combined. I hope you understand what I am asking

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For everything combined I'd just say "$m$ radical $n$." I'd call them individually the integer part and the radical part but that's just something I made up right now. – anon Sep 8 '11 at 20:09
@Templar: Do you mean $2$ times the square root of $3$, or do you mean $\sqrt[2]{3}$, "the square root of $3$" (or with $\sqrt[m]{n}$, "the $m$th root of $n$")? – Arturo Magidin Sep 8 '11 at 20:15
@ArturoMagidin I meant to ask as square root (edited), but you may answer both like $m\sqrt[k]n$ or $2\sqrt[4]3$ too – Templar Sep 8 '11 at 20:21
@Templar: The number "inside" is sometimes called the "radicand"; so $n$ and $3$ in your examples would be the "radicands". Your $m$ and $2$, which are merely multiplying the result of the radical, are simply "factors". The $m$ in $\sqrt[m]{n}$ does not, as far as I am aware, have a specific name. – Arturo Magidin Sep 8 '11 at 20:25
up vote 6 down vote accepted

The quantity inside the radical ("$\sqrt{\hspace{.1in}}$") is called the radicand. The quantity above the radical is called the index. I would call the quantity preceding the radical a coefficient, but that has nothing to do with the radical.

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