22: The expression is of the type ∞ − ∞. How come, when under each root there is another indeterminate difference? Under each root there is just one leading term, 2²ⁿ = 4ⁿ under the first root and nⁿ under the second root, and they thus prevail and determine outcomes of individual roots. These terms are of different order (the latter dominates the former), and the roots do not change this as they are of the same type (both are square roots). Thus roots are of different types and the best approach is factoring out and using the scale of powers.

One could also try to get rid of the square root algebraically, see the box "difference of roots". However, here it would be the longer way. Since the terms under the roots are of different type, there would be no cancelling after getting rid of the roots, all terms would be still there and one would have to work with powers (factoring out leading terms) anyway, but in a more complicated expression. Try it to check that it really happens.

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