`a,` `\sqrt{50}-2\sqrt{18}+\sqrt{200}-3\sqrt{162}`
`=5\sqrt{2}-6\sqrt{2}+10\sqrt{2}-27\sqrt{2}`
`=-28\sqrt{2}`
`b,` `\sqrt{8+2\sqrt{15}}+\sqrt{8-2\sqrt{15}}`
`=\sqrt{5+2\sqrt{15}+3}+\sqrt{5-2\sqrt{15}+3}`
`=\sqrt{(\sqrt{5}+\sqrt{3})^2}+\sqrt{(\sqrt{5}-\sqrt{3})^2}`
`=|\sqrt{5}+\sqrt{3}|+|\sqrt{5}-\sqrt{3}|`
`=\sqrt{5}+\sqrt{3}+\sqrt{5}-\sqrt{3}`
`=2\sqrt{5}`
`c,` `(\sqrt{21}-\sqrt{30})\sqrt{17+2\sqrt{70}}`
`=\sqrt{3}(\sqrt{7}-\sqrt{10})\sqrt{7+2\sqrt{70}+10}`
`=\sqrt{3}(\sqrt{7}-\sqrt{10})\sqrt{(\sqrt{7}+\sqrt{10})^2}`
`=\sqrt{3}(\sqrt{7}-\sqrt{10})|\sqrt{7}+\sqrt{10}|`
`=\sqrt{3}(\sqrt{7}-\sqrt{10})(\sqrt{7}+\sqrt{10})`
`=\sqrt{3}(7-10)`
`=-3\sqrt{3}`
`d,` $\text{Đặt}$ `D=\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}-2\sqrt{2}`
`⇒\sqrt{2}D=\sqrt{2}(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}-2\sqrt{2})`
`=\sqrt{2}.\sqrt{3+\sqrt{5}}-\sqrt{2}.\sqrt{3-\sqrt{5}}-\sqrt{2}.2\sqrt{2}`
`=\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}-4`
`=\sqrt{5+2\sqrt{5}+1}-\sqrt{5-2\sqrt{5}+1}-4`
`=\sqrt{(\sqrt{5}+1)^2}-\sqrt{(\sqrt{5}-1)^2}-4`
`=|\sqrt{5}+1|-|\sqrt{5}-1|-4`
`=\sqrt{5}+1-(\sqrt{5}-1)-4`
`=\sqrt{5}+1-\sqrt{5}+1-4`
`=-2`
`⇒D=-\sqrt{2}`
