[latex] \sqrt{\sqrt{8+2 \sqrt{15} } - \sqrt{8- \\ 2 \sqrt{15}} * 2+7} = ?[/latex]

[latex] \sqrt{\left (\sqrt{8+2\sqrt{15}}-\sqrt{8-2\sqrt{15}}\right )\cdot 2+7}} =\\\\=\sqrt{\left (\sqrt{(\sqrt5+\sqrt3)^2}-\sqrt{(\sqrt5-\sqrt3)^2}\right )\cdot 2+7}=\\\\=\sqrt{(|\sqrt5+\sqrt3|-|\sqrt5-\sqrt3|)\cdot 2+7}=\\\\=\sqrt{\left (\sqrt5+\sqrt3-(\sqrt5-\sqrt3)\right )\cdot 2+7}=\\\\=\sqrt{4\sqrt3+7}=\sqrt{(2+\sqrt3)^2}=|2+\sqrt3|=2+\sqrt3[/latex]