Radical difference

$\text{To find which fraction is the smallest, we just have to find whose denominator is the largest.}\\ \text{Now it's quite easily seen that}\; \sqrt{4}+\sqrt{5}>\sqrt{3}+\sqrt{4}>\sqrt{2}+\sqrt{3}>\sqrt{1}+\sqrt{2}\\ \text{Hence:}\;\boxed{\dfrac{1}{\sqrt{4}+\sqrt{5}}<\dfrac{1}{\sqrt{3}+\sqrt{4}}<\dfrac{1}{\sqrt{2}+\sqrt{3}}<\dfrac{1}{\sqrt{1}+\sqrt{2}}}$