Please Help!

Think of the perfect squares around 300. 17^2 = 289, 18^2 = 324. $\sqrt{324} = 18$ as we know, so 18 is the least integer greater than $\sqrt{300}$

$\lceil{\sqrt{300}}\rceil = \lceil{\sqrt{3 \cdot 100}}\rceil = \lceil{10 \sqrt{3}}\rceil \approx \lceil{10 \cdot 1.73}\rceil = \lceil{17.3}\rceil = \boxed{18}$