Educated guesses are not appropriate, whether you happen to get it right or not.
What parts did you do wrong deliberately?
What parts are you unable to reproduce?
What parts still do not follow a logical line of reasoning?
Lev88 is not giving you a hard time. Lev88 is trying to encourage self-confidence.
We all understand that you just want to be sure. Well, BE sure! The only problem I see with your calculations and formulas is that you do not believe. Well, answer my 3 questions. You should start to believe. About what are you not sure? Put down your vague doubts with exacting setup and calculations and reasoning. If you still have doubts, after your perfect execution, tell such doubts to go away and bother none other.
300^2 is not simpler than 90,000. It is also not less simple. There are no established criteria to determine if one thing is simpler than another. They are EXACTLY the same, as far as I am concerned. If your teacher or examiner requires the tedious multiplication, then do it. This consideration is no longer mathematics; it is pedantic semantics only.