\(a,=\left(4\sqrt{2}-15\sqrt{2}+12\sqrt{2}\right):\sqrt{2}+2=\sqrt{2}:\sqrt{2}+2=1+2=3\\ b,=\dfrac{13\sqrt{3}}{4}+\dfrac{3\sqrt{3}}{4}+2-\sqrt{3}-9\sqrt{3}=4\sqrt{3}+2-10\sqrt{3}=2-6\sqrt{3}\\ c,=\sqrt{\left(2-\sqrt{3}\right)^2}+2+\sqrt{3}=2-\sqrt{3}+2+\sqrt{3}=4\\ d,=\sqrt{13+6\sqrt{4+2\sqrt{2}-1}}=\sqrt{13+6\sqrt{\left(\sqrt{2}+1\right)^2}}\\ =\sqrt{13+6\sqrt{2}+6}=\sqrt{19+6\sqrt{2}}=3\sqrt{2}+1\)
\(e,=\dfrac{\sqrt{3}\left(\sqrt{3}+2\right)}{\sqrt{3}}+\dfrac{\sqrt{2}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}-2-\sqrt{3}\\ =\sqrt{3}+2+\sqrt{2}-2-\sqrt{3}=\sqrt{2}\)
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