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 \(3>\sqrt{5}\))