`\sqrt{11}/\sqrt{22}+\sqrt{45}/3+\sqrt{3-2\sqrt{2}}+(1+\sqrt{5})^2`
`=\sqrt{11}/(\sqrt{11}.\sqrt{2})+(3\sqrt{5})/3+\sqrt{(\sqrt{2})^2-2.\sqrt{2}.1+1^2}+(1+2\sqrt{5}+5)`
`=1/\sqrt{2}+\sqrt{5}+\sqrt{(\sqrt{2}-1)^2}+(6+2\sqrt{5})`
`=1/\sqrt{2}+\sqrt{5}+(\sqrt{2}-1)+6+2\sqrt{5}`
`=1/\sqrt{2}+\sqrt{5}+\sqrt{2}-1+6+2\sqrt{5}`
`=1/\sqrt{2}+3\sqrt{5}+\sqrt{2}+5`
`=(1+3\sqrt{10}+2+5\sqrt{2})/\sqrt{2}`
`=(3+3\sqrt{10}+5\sqrt{2})/\sqrt{2}`
`=(\sqrt{2}(3+3\sqrt{10}+5\sqrt{2}))/(\sqrt{2}.\sqrt{2})`
`=(3\sqrt{2}+6\sqrt{5}+10)/2`
