Ta có: \(\sqrt{7-3\sqrt{5}}\)

\(=\frac{\sqrt{14-6\sqrt{5}}}{\sqrt{2}}\)

\(=\frac{\sqrt{9-2\cdot3\cdot\sqrt{5}+5}}{\sqrt{2}}\)

\(=\frac{\sqrt{\left(3-\sqrt{5}\right)^2}}{\sqrt{2}}\)

\(=\frac{\left|3-\sqrt{5}\right|}{\sqrt{2}}\)

\(=\frac{3-\sqrt{5}}{\sqrt{2}}\)(Vì \(3>\sqrt{5}\))

\(\dfrac{1}{1-\sqrt{5}}+\dfrac{1}{\sqrt{5}-1}=\dfrac{-1+1}{\sqrt{5}-1}=\dfrac{0}{\sqrt{5}-1}=0\)

\(\dfrac{1}{1-\sqrt{5}}+\dfrac{1}{\sqrt{5}-1}=\dfrac{1}{1-\sqrt{5}}-\dfrac{1}{1-\sqrt{5}}=0\)

\(a,9\sqrt{5}+3\sqrt{20}-7\sqrt{45}=9\sqrt{5}+6\sqrt{5}-21\sqrt{5}=-6\sqrt{5}\\ b,\dfrac{2\sqrt{6}+\sqrt{40}}{\sqrt{3}+\sqrt{5}}=\dfrac{2\sqrt{6}+2\sqrt{10}}{\sqrt{3}+\sqrt{5}}\\ =\dfrac{2\sqrt{2}\left(\sqrt{3}+\sqrt{5}\right)\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{3}+\sqrt{5}\right)\left(\sqrt{5}-\sqrt{3}\right)}=\dfrac{2\sqrt{2}\left(5-3\right)}{5-3}=2\sqrt{2}\)

\(\left(3+\frac{\sqrt{5}}{\sqrt{10}}+\sqrt{3}+\sqrt{5}\right)-\left(3-\frac{\sqrt{5}}{\sqrt{10}}+\sqrt{3}-\sqrt{5}\right)=\sqrt{34.64911064}\)

\(B=50-3\sqrt{98}+2\sqrt{8}+3\sqrt{32}-5\sqrt{18}\)

\(=50-3.\sqrt{7^2.2}+2\sqrt{2^2.2}+3\sqrt{4^2.2}-5\sqrt{3^2.2}\)

\(=50-3.7\sqrt{2}+2.2\sqrt{2}+3.4\sqrt{2}-5.3\sqrt{2}\)

\(=50-21\sqrt{2}+4\sqrt{2}+12\sqrt{2}-15\sqrt{2}\)

\(=50+\sqrt{2}.\left(-21+4+12-15\right)\)

\(=50+\sqrt{2}.\left(-20\right)\)

\(=50-20\sqrt{2}\)

\(C=\left(\sqrt{3}+\sqrt{5}+\sqrt{7}\right)\left(\sqrt{3}+\sqrt{5}-\sqrt{7}\right)\)

\(=\left(\sqrt{3}+\sqrt{5}\right)^2-\sqrt{7}^2\)

\(=\sqrt{3}^2+2.\sqrt{3}.\sqrt{5}+\sqrt{5}^2-7\)

\(=2\sqrt{15}+3+5-7\)

\(=2\sqrt{15}+1\)