Ta có: \(\sqrt{\frac{3\sqrt{5}+5}{3\sqrt{5}-5}}\)
\(=\sqrt{\frac{\left(3\sqrt{5}+5\right)^2}{\left(3\sqrt{5}-5\right)\left(3\sqrt{5}+5\right)}}\)
\(=\sqrt{\frac{\left(3\sqrt{5}+5\right)^2}{45-25}}\)
\(=\frac{3\sqrt{5}+5}{2\sqrt{5}}\)
\(=\frac{\sqrt{5}\left(3+\sqrt{5}\right)}{2\sqrt{5}}\)
\(=\frac{3+\sqrt{5}}{2}< \frac{3+\sqrt{5}}{1}=3+\sqrt{5}\)
Vậy: \(\sqrt{\frac{3\sqrt{5}+5}{3\sqrt{5}-5}}< 3+\sqrt{5}\)
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