`1)\sqrt{4-2\sqrt{3}}=\sqrt{(\sqrt{3}-1)^2}=|\sqrt{3}-1|=\sqrt{3)-1`
`2)\sqrt{7-4\sqrt{3}}=\sqrt{(2-\sqrt{3})^2}=|2-\sqrt{3}|=2-\sqrt{3}`
`3)\sqrt{9+4\sqrt{5}}=\sqrt{(\sqrt{5}+2)^2}=|\sqrt{5}+2|=\sqrt{5}+2`
`4)\sqrt{16-6\sqrt{7}}=\sqrt{(3-\sqrt{7})^2}=|3-\sqrt{7}|=3-\sqrt{7}`
`5)\sqrt{11+6\sqrt{2}}=\sqrt{(3+\sqrt{2})^2}=|3+\sqrt{2}|=3+\sqrt{2}`
`6)\sqrt{4+2\sqrt{3}}- \sqrt{3}=\sqrt{(\sqrt{3}+1)^2}- \sqrt{3}=|\sqrt{3}+1|- \sqrt{3}=\sqrt{3)+1-\sqrt{3}=1`
`7)\sqrt{14-6\sqrt{5}}+\sqrt{5}-1=\sqrt{(3-\sqrt{5})^2}+\sqrt{5}-1=|3-\sqrt{5}|+\sqrt{5}-1=3-\sqrt{5}+\sqrt{5}-1=2`
`8)\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}=\sqrt{(\sqrt{7}-1)^2}-\sqrt{(\sqrt{7}+1)^2}=|\sqrt{7}-1|-|\sqrt{7}+1|=\sqrt{7}-1-\sqrt{7}-1=-2`
`9)\sqrt{41-12\sqrt{5}}-\sqrt{41+12\sqrt{5}}=\sqrt{(6-\sqrt{5})^2}-\sqrt{(6+\sqrt{5})^2}=|6-\sqrt{5}|-|6+\sqrt{5}|=6-\sqrt{5}-6-\sqrt{5}=-2\sqrt{5}`
`10)\sqrt{29+12\sqrt{5}}+\sqrt{29-12\sqrt{5}}=\sqrt{(2\sqrt{5}+3)^2}+\sqrt{(2\sqrt{5}-3)^2}=|2\sqrt{5}+3|+|2\sqrt{5}-3|=2\sqrt{5}+3+2\sqrt{5}-3=4\sqrt{5}`
`11)\sqrt{17+12\sqrt{2}}+\sqrt{17-12\sqrt{2}}=\sqrt{(3+2\sqrt{2})^2}+\sqrt{(3-2\sqrt{2})^2}=|3+2\sqrt{2}|+|3-2\sqrt{2}|=3+2\sqrt{2}+3-2\sqrt{2}=6`
