`#tnvt`
`f)\sqrt{7-2\sqrt{10}}+\sqrt{20}+1/2\sqrt{8}`
`=\sqrt{(\sqrt{5}-\sqrt{2})^2}+2\sqrt{5}+1/2 .2\sqrt{2}`
`=|\sqrt{5}-\sqrt{2}|+2\sqrt{5}+\sqrt{2}`
`=\sqrt{5}-\sqrt{2}+2\sqrt{5}+\sqrt{2}`
`=3\sqrt{5}`
`g)\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}`
`=\sqrt{(\sqrt{3}+\sqrt{2})^2}-\sqrt{(\sqrt{3}-\sqrt{2})^2}`
`=|\sqrt{3}+\sqrt{2}|-|\sqrt{3}-\sqrt{2}|`
`=\sqrt{3}+\sqrt{2}-\sqrt{3}+\sqrt{2}`
`=2\sqrt{2}`
`h)\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}`
`=\sqrt{(3-2\sqrt{2})^2}+\sqrt{(2\sqrt{2}+1)^2}`
`=|3-2\sqrt{2}|+|2\sqrt{2}+1|`
`=3-2\sqrt{2}+2\sqrt{2}+1`
`=4`
`i)\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}`
`=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{(3-2\sqrt{5})^2}}}`
`=\sqrt{\sqrt{5}-\sqrt{3-|3-2\sqrt{5}|}}`
`=\sqrt{\sqrt{5}-\sqrt{3-2\sqrt{5}+3}}`
`=\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}`
`=\sqrt{\sqrt{5}-\sqrt{(\sqrt{5}-1)^2}}`
`=\sqrt{\sqrt{5}-|\sqrt{5}-1|}`
`=\sqrt{\sqrt{5}-\sqrt{5}+1}`
`=\sqrt{1}=1`
`j)\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}`
`=\sqrt{13+30\sqrt{2+\sqrt{(2\sqrt{2}+1)^2}}}`
`=\sqrt{13+30\sqrt{2+|2\sqrt{2}+1|}}`
`=\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}`
`=\sqrt{13+30\sqrt{(\sqrt{2}+1)^2}}`
`=\sqrt{13+30|\sqrt{2}+1|}`
`=\sqrt{13+30+30\sqrt{2}}`
`=\sqrt{43+30\sqrt{2}}`
`=\sqrt{25+2.5.3\sqrt{2}+18}`
`=\sqrt{(5+3\sqrt{2})^2}`
`=|5+3\sqrt{2}|`
`=5+3\sqrt{2}`
