1: \(=\sqrt{3}\)
3: \(=\sqrt{5}+\sqrt{2}+\sqrt{6}-\sqrt{2}=\sqrt{6}+\sqrt{5}\)
6: \(=9+4\sqrt{5}-9-4\sqrt{5}=0\)
\(1,=\dfrac{\sqrt{3}\left(\sqrt{5}-\sqrt{2}\right)}{\sqrt{5}-\sqrt{2}}=-\sqrt{3}\\ 2,=\dfrac{\sqrt{15}}{10}+\dfrac{\sqrt{15}}{30}-\dfrac{2\sqrt{15}}{15}=\dfrac{6\sqrt{15}+2\sqrt{15}-8\sqrt{15}}{60}=0\\ 3,=\dfrac{3\left(\sqrt{5}+\sqrt{2}\right)}{3}+\dfrac{4\left(\sqrt{6}-\sqrt{2}\right)}{4}=\sqrt{5}+\sqrt{2}+\sqrt{6}-\sqrt{2}=\sqrt{5}+\sqrt{6}\\ 4,=\dfrac{\sqrt{5}+\sqrt{3}+\sqrt{5}-\sqrt{3}}{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}\cdot\sqrt{5}=\dfrac{10}{2}=5\\ 5,=\left(2\sqrt{5}-3\sqrt{5}+\sqrt{5}\right)\sqrt{5}=0\\ 6,=0\\ 7,=\left(\sqrt{5}+\sqrt{5}-\dfrac{5}{4}\cdot\dfrac{\sqrt{4+5\sqrt{5}}}{2}\right):2\sqrt{5}\\ =\left(2\sqrt{5}-\dfrac{5\sqrt{4+5\sqrt{5}}}{8}\right):2\sqrt{5}=1-\dfrac{5\sqrt{4+5\sqrt{5}}}{16\sqrt{5}}\\ =1-\dfrac{\sqrt{20+25\sqrt{5}}}{16}=\dfrac{16-\sqrt{20+25\sqrt{5}}}{16}\)
\(8,=\dfrac{4\sqrt{3}}{3}+15\sqrt{3}-3\sqrt{3}-\dfrac{20\sqrt{3}}{3}=12\sqrt{3}-\dfrac{16\sqrt{3}}{3}=\dfrac{36\sqrt{3}-16\sqrt{3}}{3}=\dfrac{20\sqrt{3}}{3}\\ 9,=12\sqrt{2}-6+2\sqrt{3}\\ 10,=\left(\sqrt{75}+\sqrt{45}\right):\sqrt{15}=\sqrt{5}+\sqrt{3}\\ 11,=\sqrt{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}=\sqrt{1}=1\\ 12,=\sqrt{\left(\sqrt{10}-1\right)\left(\sqrt{10}+1\right)}=\sqrt{9}=3\\ 13,=\dfrac{\sqrt{35}\left(\sqrt{5}-\sqrt{7}+2\sqrt{2}\right)}{\sqrt{35}}=\sqrt{5}-\sqrt{7}+2\sqrt{2}\\ 14,=\dfrac{\sqrt{3}}{2}+\dfrac{\sqrt{3}}{3}+\dfrac{\sqrt{3}}{6}=\dfrac{3\sqrt{3}+2\sqrt{3}+1}{6}=\dfrac{6\sqrt{3}}{6}=\sqrt{3}\)
