How to determine if given “complex” time complexity is $O(n^2)$?
Sometimes, you can replace them by $n$. For example, in $F_1(n) = (n+\log(n))\times \sqrt{n+\log n}$, replace $\log(n)$ by $n$. So, $F_1(n) \leqslant 2n \sqrt{2n}$ and it means $F_1(n) = O(n\sqrt{n})$. Also, in multiplication or summation, you can ignore constants (not all the time in power functions). Hence, $F_2(n) = n \times (200 + \log^2(n)) = \Theta(n
\log^2(n))$. Or in $F_3(n) = (7 + n^3) \log(n^5) = 5 \times (7 + n^3) \log(n) = \Theta(n^3 \log(n))$ (as $\log(n^c) = c \log(n)$).