a: \(\sqrt{2+\sqrt{3}}-\sqrt{2-\sqrt{3}}\)
\(=\dfrac{\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{\left(\sqrt{3}-1\right)^2}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{3}+1-\sqrt{3}+1}{\sqrt{2}}=\dfrac{2}{\sqrt{2}}=\sqrt{2}\)
b: \(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}-\sqrt{2}\)
\(=\dfrac{\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}-2}{\sqrt{2}}\)
\(=\dfrac{\sqrt{\left(\sqrt{5}+1\right)^2}-\sqrt{\left(\sqrt{5}-1\right)^2}-2}{\sqrt{2}}\)
\(=\dfrac{\sqrt{5}+1-\left(\sqrt{5}-1\right)-2}{\sqrt{2}}=\dfrac{1+1-2}{\sqrt{2}}=0\)
c: \(\sqrt{6,5+\sqrt{12}}+\sqrt{6,5-\sqrt{12}}+2\sqrt{6}\)
\(=\dfrac{\sqrt{13+2\sqrt{12}}+\sqrt{13-2\sqrt{12}}+2\sqrt{12}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{\left(2\sqrt{3}+1\right)^2}+\sqrt{\left(2\sqrt{3}-1\right)^2}+2\cdot2\sqrt{3}}{\sqrt{2}}\)
\(=\dfrac{2\sqrt{3}+1+2\sqrt{3}-1+4\sqrt{3}}{\sqrt{2}}=\dfrac{8\sqrt{3}}{\sqrt{2}}=\dfrac{8\sqrt{6}}{2}=4\sqrt{6}\)
