a: \(=\sqrt{20+2\cdot2\sqrt{5}\cdot1+1}=\sqrt{\left(2\sqrt{5}+1\right)^2}=2\sqrt{5}+1\)
b: \(=\dfrac{1}{\sqrt{2}}\left(\sqrt{18+2\sqrt{17}}-\sqrt{18-2\sqrt{17}}\right)\)
\(=\dfrac{1}{\sqrt{2}}\left(\sqrt{17}+1-\sqrt{17}+1\right)=\dfrac{2}{\sqrt{2}}=\sqrt{2}\)
c: \(=\sqrt{\left(3-\sqrt{7}\right)^2}-\sqrt{\left(5+\sqrt{7}\right)^2}\)
\(=3-\sqrt{7}-5-\sqrt{7}=-2\sqrt{7}-2\)
d: \(=\sqrt{6+2\sqrt{2}\cdot\sqrt{3-\sqrt{3}-1}}\)
\(=\sqrt{6+2\cdot\sqrt{4-2\sqrt{3}}}\)
\(=\sqrt{6+2\left(\sqrt{3}-1\right)}=\sqrt{4+2\sqrt{3}}=\sqrt{3}+1\)
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