\(\left(\sqrt{35}+5\right)\sqrt{6-\sqrt{35}}=\frac{\left(\sqrt{35}+5\right)\sqrt{2}\sqrt{6-\sqrt{35}}}{\sqrt{2}}\)
\(=\frac{\sqrt{5}.\left(\sqrt{7}+\sqrt{5}\right)\sqrt{12-2\sqrt{35}}}{\sqrt{2}}=\frac{\sqrt{5}.\left(\sqrt{7}+\sqrt{5}\right)\sqrt{7-2\sqrt{7}\sqrt{5}+5}}{\sqrt{2}}\)
\(=\frac{\sqrt{5}.\left(\sqrt{7}+\sqrt{5}\right)\sqrt{\left(\sqrt{7}-\sqrt{5}\right)^2}}{\sqrt{2}}=\frac{\sqrt{5}.\left(\sqrt{7}+\sqrt{5}\right)\left(\sqrt{7}-\sqrt{5}\right)}{\sqrt{2}}\)
\(=\frac{\sqrt{5}.\left(7-5\right)}{\sqrt{2}}=\frac{\sqrt{5}.2}{\sqrt{2}}=\sqrt{10}\)
\(=\sqrt{35}.\sqrt{6-\sqrt{35}}+5\sqrt{6-\sqrt{35}}=\sqrt{210-35\sqrt{35}}+\sqrt{150-25\sqrt{35}}\)
\(=\left(\sqrt{35}+6-1\right)\sqrt{6-\sqrt{35}}=\left(6+\sqrt{35}\right)\sqrt{6-\sqrt{35}}-\sqrt{6-\sqrt{35}}\)
= \(\sqrt{6+\sqrt{35}}\left(36-35\right)-\sqrt{6-\sqrt{35}}=\sqrt{6+\sqrt{35}}-\sqrt{6-\sqrt{35}}=A\)
A^2 = \(6+\sqrt{35}+6-\sqrt{35}-2\sqrt{\left(6+\sqrt{35}\right)\left(6-\sqrt{35}\right)}=12-2=10\)
=>A = căn 10
