0\; \; \Rightarrow \\\\\\\sqrt{4+\sqrt7}-\sqrt{4-\sqrt7}=+\sqrt2 " alt=" \Big (\sqrt{4+\sqrt7}-\sqrt{4-\sqrt7}\Big )^2=\\\\=(4+\sqrt7)-2\cdot \sqrt{(4+\sqrt7)(4-\sqrt7)}+(4-\sqrt7)=\\\\=8-2\cdot \sqrt{4^2-(\sqrt7)^2}=8-2\cdot \sqrt{16-7}=8-2\cdot \sqrt9=\\\\=8-2\cdot 3=8-6=2\\\\\\\sqrt7\approx2,65\; \; \to \; \; 4-\sqrt7\approx 1,35\; ,\; \; \sqrt{4-\sqrt7}\approx \sqrt{1,35}\approx 1,16\\\\\sqrt{4+\sqrt7}\approx 2,31\; \; \Rightarrow \; \; \Big (\sqrt{4+\sqrt7}}-\sqrt{4-\sqrt7}\Big )\approx 2,31-1,16>0\; \; \Rightarrow \\\\\\\sqrt{4+\sqrt7}-\sqrt{4-\sqrt7}=+\sqrt2 " align="absmiddle" class="latex-formula">