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$$\sqrt{\ 16\ +\ 2\sqrt{\ 55}}$$ can be seen as the square root of 16 + $$2\sqrt{\ 55}$$
Now on observing 16 + $$2\sqrt{\ 55}$$, we can see it as an expansion of $$(a+b)^2$$: a being $$\sqrt{11\ }$$ and b being $$\sqrt{5\ }$$.
Hence, we can rewrite the equation as $$\left(\sqrt{\ 11}+\sqrt{\ 5}\right)^2$$ , whose square root is $$\sqrt{\ 11}$$+$$\sqrt{\ 5}$$.
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