Упростить выражение. 1) [latex] \sqrt{7+4 \sqrt{3} } [/latex] 2) [latex] \sqrt{6-2 \sqrt{5} } [/latex] 3) [latex] \sqrt{5+2 \sqrt{6} } [/latex] 4) [latex] \sqrt{3- \sqrt{8} } [/latex]

1) [latex]\sqrt{7+4\sqrt{3}}=\sqrt{4+2*2\sqrt{3}+3}=\sqrt{2^2+2*2\sqrt{3}+(\sqrt{3})^2}=\\=\sqrt{(2+\sqrt{3})^2}=2+\sqrt{3}[/latex] 2) [latex]\sqrt{6-2\sqrt{5}}=\sqrt{5-2\sqrt{5}+1}=\sqrt{(\sqrt{5})^2-2*1*\sqrt{5}+1^2}=\\=\sqrt{(\sqrt{5}-1)^2}=\sqrt{5}-1[/latex] 3) [latex]\sqrt{5+2\sqrt{6}}=\sqrt{2+2\sqrt{6}+3}=\sqrt{(\sqrt{2})^2+2*\sqrt{2}*\sqrt{3}+(\sqrt{3})^2}=\\=\sqrt{(\sqrt{2}+\sqrt{3})^2}=\sqrt{2}+\sqrt{3}[/latex] 4) [latex]\sqrt{3-\sqrt{8}}=\sqrt{2-2\sqrt{2}+1}=\sqrt{(\sqrt{2})^2-2*1*\sqrt{2}+1^2}=\\=\sqrt{(\sqrt{2}-1)^2}=\sqrt{2}-1[/latex]