\(A=\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}=\sqrt{2}+1-\sqrt{2}+1=2\\ B=\left(\sqrt{5}+1\right)\sqrt{\dfrac{6-2\sqrt{5}}{2}}=\left(\sqrt{5}+1\right)\cdot\dfrac{\sqrt{5}-1}{2}=\dfrac{4}{2}=2\\ C=\sqrt{\dfrac{\left(3\sqrt{3}-4\right)\left(2\sqrt{3}-1\right)}{11}}-\sqrt{\dfrac{\left(\sqrt{3}+4\right)\left(5+2\sqrt{3}\right)}{13}}\\ C=\sqrt{\dfrac{22-11\sqrt{3}}{11}}-\sqrt{\dfrac{26+13\sqrt{3}}{13}}\\ C=\sqrt{\dfrac{4-2\sqrt{3}}{2}}-\sqrt{\dfrac{4+2\sqrt{3}}{2}}\\ C=\dfrac{\sqrt{3}-1-\sqrt{3}-1}{\sqrt{2}}=\dfrac{-2}{\sqrt{2}}=-\sqrt{2}\)
\(D=\sqrt{8+2\sqrt{15}}-\sqrt{\dfrac{8-2\sqrt{15}}{1}}\\ D=\sqrt{3}+\sqrt{5}-\sqrt{3}+\sqrt{5}=2\sqrt{5}\\ E=\sqrt{5}-\sqrt{3-2\sqrt{5}+3}\\ E=\sqrt{5}-\sqrt{6-2\sqrt{5}}=\sqrt{5}-\sqrt{5}+1=1\\ F=\sqrt{6+2\sqrt{2}\cdot\sqrt{3-\sqrt{3}-1}}\\ F=\sqrt{6+2\sqrt{4-2\sqrt{3}}}=\sqrt{6+2\left(\sqrt{3}-1\right)}\\ F=\sqrt{4+2\sqrt{3}}=\sqrt{3}+1\)
\(G=\sqrt{\dfrac{8+2\sqrt{15}}{2}}+\sqrt{\dfrac{8-2\sqrt{15}}{2}}-\sqrt{2}\sqrt{6-2\sqrt{5}}\\ G=\dfrac{\sqrt{3}+\sqrt{5}+\sqrt{3}-\sqrt{5}}{\sqrt{2}}-\sqrt{2}\left(\sqrt{5}-1\right)\\ G=\dfrac{2\sqrt{3}}{\sqrt{2}}-\sqrt{10}+\sqrt{2}=\sqrt{6}-\sqrt{10}+\sqrt{2}\)
