a: \(\dfrac{1}{2\sqrt{2}-3\sqrt{3}}=\dfrac{2\sqrt{2}+3\sqrt{3}}{\left(2\sqrt{2}-3\sqrt{3}\right)\left(2\sqrt{2}+3\sqrt{3}\right)}\)
\(=\dfrac{2\sqrt{2}+3\sqrt{3}}{8-27}=\dfrac{-2\sqrt{2}-3\sqrt{3}}{19}\)
b: \(\sqrt{\dfrac{3-\sqrt{5}}{3+\sqrt{5}}}=\sqrt{\dfrac{\left(3-\sqrt{5}\right)^2}{\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)}}\)
\(=\sqrt{\dfrac{\left(3-\sqrt{5}\right)^2}{9-5}}=\dfrac{\sqrt{\left(3-\sqrt{5}\right)^2}}{\sqrt{4}}=\dfrac{3-\sqrt{5}}{2}\)
c: \(\dfrac{\sqrt{8}}{\sqrt{5}-\sqrt{3}}=\dfrac{\sqrt{8}\left(\sqrt{5}+\sqrt{3}\right)}{5-3}\)
\(=\dfrac{2\sqrt{2}\left(\sqrt{5}+\sqrt{3}\right)}{2}=\sqrt{2}\left(\sqrt{5}+\sqrt{3}\right)\)
d: \(\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}=\sqrt{\dfrac{\left(2-\sqrt{3}\right)^2}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}}\)
\(=\sqrt{\dfrac{\left(2-\sqrt{3}\right)^2}{1}}=\left|2-\sqrt{3}\right|=2-\sqrt{3}\)
