I have written $$\sqrt{2-\sqrt{2\overline{-\sqrt2}}}$$ for $$\sqrt{2-\sqrt{2-\sqrt{2-\sqrt{2-\sqrt{2-\sqrt{2-\sqrt{2...}}}}}}}$$
[Just care the overline above last $\overline{- \sqrt2}$]
I have taken second radical because it links to another operation. Someone math scholar says, that is not standard format of notation. Is there any standard format of notation for this?
You can write it as a recurrence: $$f(n + 1) = \sqrt{2 - f(n)}; f(0) = \sqrt{2}$$ And then once you've established that, you can now write: $$\lim_{n\rightarrow\infty}f(n) = \sqrt{2 - \sqrt{2 - \sqrt{2 - \sqrt{2...}}}}$$ Which allows you to use $\lim_{n\rightarrow\infty}f(n)$ as a shorthand.