Evaluate $\left\lceil {-\!\sqrt{23}}\right\rceil$.
I need to find the smallest integer that is greater than or equal to $-\!\sqrt{23}$. I know that $\sqrt{23}$ is between 4 and 5, since $4^2 = 16$ and $5^2 = 25$. So, $-\!\sqrt{23}$ is between -5 and -4, and the smallest integer that is greater than or equal to it is -4. Therefore, $\left\lceil {-\!\sqrt{23}}\right\rceil = -4$. 