a) \(2\sqrt{3}\left(\sqrt{2}-1\right)+\left(1+\sqrt{3}\right)^2-2\sqrt{6}\)
\(=2\sqrt{6}-2\sqrt{3}+1+2\sqrt{3}+3-2\sqrt{6}=4\)
b) \(\sqrt{2-\sqrt{2}}\cdot\sqrt{2+\sqrt{2}}\cdot\sqrt{8}=4\sqrt{2}\)
c) \(\left(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)^2=3-\sqrt{5}+4+3+\sqrt{5}=10\)
d) \(\dfrac{\sqrt{10}+\sqrt{6}}{2\sqrt{5}+\sqrt{12}}=\dfrac{\left(\sqrt{10}+\sqrt{6}\right)\left(\sqrt{5}-\sqrt{3}\right)}{2\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}=\dfrac{5\sqrt{2}-3\sqrt{2}}{4}=\dfrac{\sqrt{2}}{2}\)
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