`\sqrt{6+2\sqrt{8\sqrt{2}}-9-\sqrt{7-\sqrt{2}}`
`=\sqrt{(\sqrt{7-\sqrt{2}})+\sqrt{\sqrt{2}-1}})^2-\sqrt{7-\sqrt{2}}`
`=|\sqrt{7-\sqrt{2}}+\sqrt{\sqrt{2}-1}|-\sqrt{7-\sqrt{2}`
`=(\sqrt{7-\sqrt{2}}+\sqrt{\sqrt{2}-1})-\sqrt{7-\sqrt{2}}`
`=\sqrt{7-\sqrt{2}}+\sqrt{\sqrt{2}-1}-\sqrt{7-\sqrt{2}}`
`=\sqrt{\sqrt{2}-1}`