`\qquad \sqrt{21-6\sqrt{6}}+\sqrt{9+2\sqrt{18}-2\sqrt{6+3\sqrt{3}}`
`=(\sqrt{42-12\sqrt{6}}+\sqrt{18+4\sqrt{18}}-2\sqrt{12+6\sqrt{3}})/\sqrt{2}`
`=(\sqrt{6-2.6.\sqrt{6}+36}+\sqrt{12+2.2\sqrt{3}.\sqrt{6}+6}-2\sqrt{9+2.3.\sqrt{3}+3})/\sqrt{2}`
`=(\sqrt{(6-\sqrt{6})^2}+\sqrt{(2\sqrt{3}+\sqrt{6})^2}-2\sqrt{(3+\sqrt{3})^2})/\sqrt{2}`
`=(6-\sqrt{6}+2\sqrt{3}+\sqrt{6}-2(3+\sqrt{3}))/\sqrt{3}`
`=(6+2\sqrt{3}-6-2\sqrt{3})/\sqrt{3}`
`=0`(đpcm)
