19: The expression is of the type "infinity times something", so first it is necessary to determine the "something". It is of the type ∞ − ∞. The leading term under the root is n², so when the root is taken into account, the first term behaves like n when n goes to infinity, that is, it is of the same order as the second term "-n". In intuitive calculations the leading terms cancel out

so we know that factoring out would not help.

Instead the best bet seems to be getting rid of the square root algebraically, see the box "difference of roots".

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