4: After substituting in the limit point you should find that the expression is of the type ∞ − ∞. The leading term under the inside root is x⁴, so when the root is taken into account, the root behaves like x². This is exactly like the other power under the outside root, therefore taken together they are still of order x². When we take the outer root into account, we see that the whole roots term behaves like x when x goes to infinity, that is, it is of the same order as the second term "-x". Thus there is a danger that factoring out would not help, this happens if the terms cancel. We try it.

Yes, dominant terms cancel and so 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".

Next hint
Answer