\(1)\sqrt{2-\sqrt{3}}\cdot\sqrt{2}\\ =\sqrt{4-2\sqrt{3}}\\ =\sqrt{1-2\sqrt{3}+3}\\ =\sqrt{\left(1-\sqrt{3}\right)^2}\\ =\left|1-\sqrt{3}\right|\\ =\sqrt{3}-1\left(vì\sqrt{3}>1\right)\)
\(2)\sqrt{4+\sqrt{15}}\cdot\sqrt{2}\\ =\sqrt{8+2\sqrt{15}}\\ =\sqrt{3+2\sqrt{15}+5}\\ =\sqrt{\left(\sqrt{3}+\sqrt{5}\right)^2}\\ =\left|\sqrt{3}+\sqrt{5}\right|\\ =\sqrt{3}+\sqrt{5}\)
\(3)\sqrt{5-\sqrt{21}}\cdot\sqrt{2}\\ =\sqrt{10-2\sqrt{21}}\\ =\sqrt{7-2\sqrt{21}+3}\\ =\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}\\= \left|\sqrt{7}-\sqrt{3}\right|\\ =\sqrt{7}-\sqrt{3}\)
\(4)\sqrt{6-\sqrt{35}}\cdot\sqrt{2}\\ =\sqrt{12-2\sqrt{35}}\\ =\sqrt{7-2\sqrt{35}+5}\\ =\sqrt{\left(\sqrt{7}-\sqrt{5}\right)^2}\\=\left|\sqrt{7}-\sqrt{5}\right|\\ =\sqrt{7}-\sqrt{5}\)
\(5)\sqrt{2+\sqrt{3}}\cdot\sqrt{2}\\ =\sqrt{4+2\sqrt{3}}\\ =\sqrt{1+2\sqrt{3}+3}\\ =\sqrt{\left(\sqrt{1}+\sqrt{3}\right)^2}\\ =\left|1+\sqrt{3}\right|\\ =1+\sqrt{3}\\ 6)\sqrt{4-\sqrt{15}}\cdot\sqrt{2}\\ =\sqrt{8-2\sqrt{15}}\\ =\sqrt{5-2\sqrt{15}+3}\\ =\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}\\ =\left|\sqrt{5}-\sqrt{3}\right|\\ =\sqrt{5}-\sqrt{3}\)
\(7)\sqrt{5+\sqrt{21}}\cdot\sqrt{2}\\ =\sqrt{10+2\sqrt{21}}\\ =\sqrt{7+2\sqrt{21}+3}\\ =\sqrt{\left(\sqrt{7}+\sqrt{3}\right)^2}\\ =\left|\sqrt{7}+\sqrt{3}\right|\\ =\sqrt{7}+\sqrt{3}\)
\(8)\sqrt{6+\sqrt{35}}\cdot\sqrt{2}\\ =\sqrt{12+2\sqrt{35}}\\ =\sqrt{7+2\sqrt{35}+5}\\ =\sqrt{\left(\sqrt{7}+\sqrt{5}\right)^2}\\ =\left|\sqrt{7}+\sqrt{5}\right|\\ =\sqrt{7}+\sqrt{5}\)
