\(\sqrt{3-\sqrt{5}}.\left(\sqrt{6}-\sqrt{8}\right)\sqrt{6+2\sqrt{5}}=\frac{\sqrt{6-2\sqrt{5}}}{\sqrt{2}}.\sqrt{2}\left(\sqrt{3}-\sqrt{4}\right).\sqrt{6+2\sqrt{5}}=\sqrt{6^2-\left(2\sqrt{5}\right)^2}.\left(\sqrt{3}-\sqrt{4}\right)=4\left(\sqrt{3}-2\right)\)
\(\sqrt{3-\sqrt{5}}\).(\(\sqrt{6}-\sqrt{8}\))\(\sqrt{6+2\sqrt{5}}\)
=\(\sqrt{\frac{1}{2}\left(6-2\sqrt{5}\right)}\).(\(\sqrt{6}-\sqrt{8}\))\(\sqrt{5+2\sqrt{5}+1}\)
=\(\sqrt{\frac{1}{2}\left(5-2\sqrt{5}+1\right)}\).(\(\sqrt{6}-\sqrt{8}\))\(\sqrt{\left(\sqrt{5}+1\right)^2}\)
=\(\sqrt{\frac{1}{2}\left(\sqrt{5}-1\right)^2}\).(\(\sqrt{6}-\sqrt{8}\))(\(\sqrt{5}+1\))
=\(\frac{\left(\sqrt{5}-1\right)}{\sqrt{2}}\).(\(\sqrt{5}+1\))(\(\sqrt{6}-\sqrt{8}\))
=\(\frac{\left(5-1\right)}{\sqrt{2}}\).(\(\sqrt{6}-\sqrt{8}\))
=3.(\(\frac{\sqrt{6}}{\sqrt{2}}\)-\(\frac{\sqrt{8}}{\sqrt{2}}\))
=3.(\(\sqrt{3}\)-\(\sqrt{4}\))
=3.(\(\sqrt{3}\)-2)
