I am struggling to write a formal proof for the following problem. I know that you can multiply by the conjugate and the get the sum of the two square roots over the quantity one. Then goes to infinity and also goes to infinity, thus the sum goes to infinity. If the whole denominator goes to infinity, then one over the denominator goes to zero.

However, I don't know if that is a sufficient proof. I would appreciate any further insight anyone can offer. Thank you in advance.

Problem:

Show that .