\(\dfrac{\sqrt{88}}{\sqrt{22}}=\sqrt{\dfrac{88}{22}}=\sqrt{4}=2\\ \dfrac{1}{3}.\sqrt{72}-3.\sqrt{50}-\dfrac{\sqrt{66}}{\sqrt{33}}\\ =\dfrac{1}{3}.\sqrt{36}.\sqrt{2}-3.\sqrt{25}.\sqrt{2}-\sqrt{\dfrac{66}{33}}\\ =\dfrac{1}{3}.6.\sqrt{2}-3.5.\sqrt{2}-\sqrt{2}\\ =\left(\dfrac{1}{3}.6-3.5-1\right).\sqrt{2}=-14\sqrt{2}\\ \dfrac{5-\sqrt{3}}{\sqrt{3}-1}=\dfrac{\left(5-\sqrt{3}\right)\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}=\dfrac{5\sqrt{3}-3+5-\sqrt{3}}{\sqrt{3}^2-1^2}\\ =\dfrac{4\sqrt{3}+2}{2}=2\sqrt{3}+1\)
\(\sqrt{50}-3\sqrt{98}+2\sqrt{8}+3\sqrt{32}-5\sqrt{18}\\ =\sqrt{25}.\sqrt{2}-3.\sqrt{49}.\sqrt{2}+2.\sqrt{4}.\sqrt{2}+3.\sqrt{16}.\sqrt{2}-5.\sqrt{9}.\sqrt{2}\\ =\left(5-3.7+2.2+3.4-5.3\right).\sqrt{2}=-15\sqrt{2}\\ 14-6\sqrt{5}+\sqrt{\left(2-\sqrt{5}\right)^2}=14-6\sqrt{5}+\left|2-\sqrt{5}\right|\\ =14-6\sqrt{5}+\sqrt{5}-2=12-5\sqrt{5}\)
