\(C.\sqrt{2}=\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}=\sqrt{\left(\sqrt{7}-1\right)^2}-\sqrt{\left(\sqrt{7}+1\right)^2}=\sqrt{7}-1-\sqrt{7}-1=-2\)
=> \(C=-\sqrt{2}\)
\(D.\sqrt{2}=\sqrt{8-2\sqrt{7}}+\sqrt{4-2\sqrt{3}}=\sqrt{\left(\sqrt{7}-1\right)^2}+\sqrt{\left(\sqrt{3}-1\right)^2}=\sqrt{7}-1+\sqrt{3}-1\)
=> \(D=\frac{\sqrt{7}+\sqrt{3}-2}{\sqrt{2}}\)
\(C=\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)
\(\Rightarrow\sqrt{2}.C=\sqrt{2}\sqrt{4-\sqrt{7}}-\sqrt{2}\sqrt{4+\sqrt{7}}\)
\(=\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}\)
\(=\sqrt{7-2\sqrt{7}+1}-\sqrt{7+2\sqrt{7}+1}\)
\(=\sqrt{\left(\sqrt{7}-1\right)^2}-\sqrt{\left(\sqrt{7}+1\right)^2}\)
\(=\sqrt{7}-1-\left(\sqrt{7}+1\right)\)
\(=\sqrt{7}-1-\sqrt{7}-1=-2\)
\(\Rightarrow C=\frac{-2}{\sqrt{2}}=-\sqrt{2}\)
\(D=\sqrt{4-\sqrt{7}}+\sqrt{2-\sqrt{3}}\)
\(\Rightarrow\sqrt{2}.D=\sqrt{2}\sqrt{4-\sqrt{7}}+\sqrt{2}\sqrt{2-\sqrt{3}}\)
\(=\sqrt{8-2\sqrt{7}}+\sqrt{4-2\sqrt{3}}\)
\(=\sqrt{7-2\sqrt{7}+1}+\sqrt{3-2\sqrt{3}+1}\)
\(=\sqrt{\left(\sqrt{7}-1\right)^2}+\sqrt{\left(\sqrt{3}-1\right)^2}\)
\(=\sqrt{7}-1+\sqrt{3}-1\)
\(=\sqrt{7}+\sqrt{3}-2\)
\(\Rightarrow D=\frac{\sqrt{7}+\sqrt{3}-2}{\sqrt{2}}=\frac{\sqrt{14}+\sqrt{6}-2\sqrt{2}}{2}\)
\(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)
\(\sqrt{16}-\sqrt{\sqrt{49}}\)
\(\sqrt{16}-\sqrt{7}\)
\(\sqrt{9}=3\)
