`#tnvt`
`a)\sqrt{14-8\sqrt{3}}`
`=\sqrt{8-8\sqrt{3}+6}`
`=\sqrt{(2\sqrt{2})^2-2.2\sqrt{2}.\sqrt{6}+\sqrt{6}^2}`
`=\sqrt{(2\sqrt{2}-\sqrt{6})^2}`
`=|2\sqrt{2}-\sqrt{6}|`
`=2\sqrt{2}-\sqrt{6}`
`b)\sqrt{17-12\sqrt{2}}`
`=\sqrt{9-12\sqrt{2}+8}`
`=\sqrt{3^2-2.3.2\sqrt{2}+(2\sqrt{2})^2}`
`=\sqrt{(3-2\sqrt{2})^2]`
`=|3-2\sqrt{2}|`
`=3-2\sqrt{2}`
`c)\sqrt{25+4\sqrt{6}}`
`=\sqrt{24+4\sqrt{6}+1}`
`=\sqrt{(2\sqrt{6})^2+2.2\sqrt{6}.1+1^2}`
`=\sqrt{(2\sqrt{6}+1)^2}`
`=|2\sqrt{6}+1|`
`=2\sqrt{6}+1`
