Question 18
Prove that the following equation holds for all non-negative integers $n$:
$$
\lfloor \sqrt{n} + \sqrt{n+1} + \sqrt{n+2} \rfloor = \lfloor \sqrt{9n} + 8 \rfloor.
$$
$$
\lfloor \sqrt{n} + \sqrt{n+1} + \sqrt{n+2} \rfloor = \lfloor \sqrt{9n} + 8 \rfloor.
$$