18: After substituting in the limit point you should find that the expression is of the type ∞ − ∞. The leading term under the inside root is n⁴, so when the root is taken into account, the root behaves like n². This is exactly like the other power under the outside root, therefore taken together they are still of order n². When we take the outer root into account, we see that the whole roots term behaves like n when n goes to infinity, that is, it is of the same order as the second term "-n". However, note that here the intuitive calculation would not make the leading term disappear,

This means that we can use factoring out of the leading term to get relatively cheaply the confirmation of our guess.

It is also possible to get rid of the square root algebraically, see the box "difference of roots". However, it would not rid us of the leading term and thus it would lead to long calculations.

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