a)Có: \(\sqrt{2}\cdot\sqrt{7+3\sqrt{5}}\)
\(=\sqrt{14+6\sqrt{5}}=\sqrt{9+2\cdot3\cdot\sqrt{5}+5}=\sqrt{\left(3+\sqrt{5}^2\right)}=3+\sqrt{5}\)
=> \(\sqrt{7+3\sqrt{5}}=\frac{3+\sqrt{5}}{\sqrt{2}}\)
b)\(\sqrt{118+28\sqrt{10}}\)
\(=\sqrt{2\left(59+14\sqrt{10}\right)}\)
\(=\sqrt{2\left(49+2\cdot7\cdot\sqrt{10}+10\right)}\)
\(=\sqrt{2\left(7+\sqrt{10}\right)^2}\)
\(=\sqrt{2}\left(7+\sqrt{10}\right)\)
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