Question

{ \left( \sqrt{ 4- \sqrt{ 7 \phantom{\tiny{!}}} \phantom{\tiny{!}}} - \sqrt{ 4+ \sqrt{ 7 \phantom{\tiny{!}}} \phantom{\tiny{!}}} \right) }^{ 2 }

Answer 1

$(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}})^{2}=4-\sqrt{7}-2\sqrt{(4-\sqrt{7})(4+\sqrt{7})} +4+\sqrt{7}=\\\\=8-2\sqrt{16-7}=8-2\sqrt{9}=8-2*3=\boxed2$