Упростить     [latex]\sqrt[8]{97-56\sqrt{3}}[/latex]

= ∜((√48)-7)=∜-(√3-2)^2=√(2-√3)=√(√3-1)^2/2=(√3-1)/√2=(√6-√2)/2

[latex]\sqrt[8] {97-56\sqrt{3}}=\\ \sqrt[8] {48-56\sqrt{3}+49}=\\ \sqrt[8] {(4\sqrt{3})^2-2*(4\sqrt{3})*7+7^2}=\\ \sqrt[8] {((4\sqrt{3})^2-7)^2}=\\ \sqrt[4] {|4\sqrt{3}-7|}=\\ \sqrt[4] {7-4\sqrt{3})}=\\ \sqrt[4] {4-4\sqrt{3})+3}=\\ \sqrt[4] {2^2-2*2*\sqrt{3})+(\sqrt{3})^2}=\\ \sqrt[4] {(2-\sqrt{3})^2}=\\ \sqrt {|2-\sqrt{3}|}=\\[/latex] [latex]\sqrt {2-\sqrt{3}}=\\ \frac{\sqrt{(2-\sqrt{3})*\sqrt{2}}}{\sqrt{2}}=\\ \frac{\sqrt {4-2\sqrt{3}}*\sqrt{2}}{2}=\\ \frac{(\sqrt {1-2\sqrt{3}+3})*\sqrt{2}}{2}=\\ \frac{(\sqrt {1^2-2*1*\sqrt{3}+(\sqrt{3})^2})*\sqrt{2}}{2}=\\ \frac{(\sqrt {(1-\sqrt{3})^2})*\sqrt{2}}{2}=\\ \frac{(|1-\sqrt{3}|)*\sqrt{2}}{2}=\\ \frac{(\sqrt{3}-1)*\sqrt{2}}{2}=\\ \frac{\sqrt{6}-\sqrt{2}}{2}[/latex]