9: After substituting in the limit point you should find that the expression in the parentheses is of the type ∞ − ∞. The leading term under the first root is n², so when the fourth root is taken into account, the whole root behaves like n^1/2 when n goes to infinity, that is, it is of the same order as the second term. 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 fourth root algebraically, see the box "difference of roots". While there is an identity for the fourth root, pretty much nobody remembers it (including the author of these pages). Fortunately, the fourth root can be got rid of by squaring twice, so it is possible to use the identity for square root twice. Try it.

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