`#tnvt`
`B=\sqrt{3-2\sqrt{2}}-\sqrt{22+12\sqrt{2}}`
`=\sqrt{(\sqrt{2}-1)^2}-\sqrt{(\sqrt{18}+\sqrt{4})^2}`
`=|\sqrt{2}-1|-|3\sqrt{2}+2|`
`=\sqrt{2}-1-3\sqrt{2}-2`
`=-2\sqrt{2}-3`
`P=\sqrt{16-8\sqrt{3}}-\sqrt{7-4\sqrt{3}}`
`=\sqrt{(\sqrt{12}-\sqrt{4})^2}-\sqrt{(\sqrt{4}-\sqrt{3})^2}`
`=|2\sqrt{3}-2|-|2-\sqrt{3}|`
`=2\sqrt{3}-2-2+\sqrt{3]`
`=3\sqrt{3}-4`
`Q=\sqrt{31-12\sqrt{3}}+\sqrt{4+2\sqrt{3}}`
`=\sqrt{(\sqrt{27}-\sqrt{4})^2}+\sqrt{(\sqrt{3}+1)^2}`
`=|3\sqrt{3}-2|+|\sqrt{3}+1|`
`=3\sqrt{3}-2+\sqrt{3}+1`
`=4\sqrt{3}-1`
