1) \(2\sqrt{50}-3\sqrt{2}+2\sqrt{8}\)
\(=10\sqrt{2}-3\sqrt{2}+4\sqrt{2}\)
\(=\left(10-3+4\right)\sqrt{2}\)
\(=11\sqrt{2}\)
2) \(4\sqrt{27}-5\sqrt{3}-2\sqrt{12}\)
\(=12\sqrt{3}-5\sqrt{3}-4\sqrt{3}\)
\(=\left(12-5-4\right)\sqrt{3}\)
\(=3\sqrt{3}\)
3) \(3\sqrt{\dfrac{2}{3}}+2\sqrt{6}-4\sqrt{\dfrac{3}{2}}\)
\(=\sqrt{6}+2\sqrt{6}-2\sqrt{6}\)
\(=\sqrt{6}\)
4) \(\sqrt{15-2\sqrt{26}}\)
\(=\sqrt{\left(\sqrt{13}\right)^2-2\sqrt{13}\sqrt{2}+\left(\sqrt{2}\right)^2}\)
\(=\sqrt{\left(\sqrt{13}-\sqrt{2}\right)^2}\)
\(=\left|\sqrt{13}-\sqrt{2}\right|\)
\(\sqrt{13}-\sqrt{2}\)
5) \(\dfrac{1}{\sqrt{5}-\sqrt{3}}+\dfrac{1}{\sqrt{5}+\sqrt{3}}\)
\(=\dfrac{\sqrt{5}+\sqrt{3}+\sqrt{5}-\sqrt{3}}{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}\)
\(=\dfrac{2\sqrt{5}}{2}=2\)