\(=\sqrt{40-2\sqrt{21\cdot16}}+\sqrt{19-2\sqrt{84}}\)
\(=2\sqrt{7}-2\sqrt{3}+2\sqrt{3}-\sqrt{7}=\sqrt{7}\)
\(\sqrt{40-8\sqrt{21}}+\sqrt{19-4\sqrt{21}}\)
\(=\sqrt{28-2.\sqrt{28.12}+12}+\sqrt{12-2.\sqrt{12.7}+7}\)
\(=\sqrt{\left(\sqrt{28}-\sqrt{12}\right)^2}+\sqrt{\left(\sqrt{12}-\sqrt{7}\right)^2}\)
\(=\sqrt{28}-\sqrt{12}+\sqrt{12}-\sqrt{7}\)
\(=\sqrt{28}-\sqrt{7}=2\sqrt{7}-\sqrt{7}=\sqrt{7}\)
`\sqrt{40-8\sqrt{21}}+\sqrt{19-4\sqrt{21}}`
`=\sqrt{(2\sqrt{7}-2\sqrt{3})^2}+\sqrt{(2\sqrt{3}-\sqrt{7})^2}`
`=2\sqrt{7}-2\sqrt{3}+2\sqrt{3}-\sqrt{7}`
`=\sqrt{7}`
