proooooooosze o pomoc oblicz: [latex]( sqrt{2-1} + sqrt{ sqrt{2+1} } ) ^{2} [/latex] [latex]2 sqrt{2} +4 sqrt[4]{4} +8 sqrt[6]{8} [/latex]

[latex]a)\ \( sqrt{2-1} + sqrt{ sqrt{2+1} } ) ^{2} =\ \=( sqrt{1} + sqrt{ sqrt{3} } ) ^{2} =(sqrt{1})^2 +2*sqrt{1}*sqrt{sqrt{3}}+(sqrt{sqrt{3}})^2=\ \=1+2sqrt[4]{3}+sqrt{3}[/latex] [latex]b)\ \2 sqrt{2} +4 sqrt[4]{4} +8 sqrt[6]{8} =2 sqrt{2} +4 sqrt[4]{2^2} +8 sqrt[6]{2^3} =\ \=2 sqrt{2} +4 *(2^2)^{frac{1}{4}} +8 *(2^3)^{frac{1}{6}}=2 sqrt{2} +4 *2^{frac{1}{2}} +8 *2^{frac{1}{2}}=\ \ =2 sqrt{2} +4 sqrt{2} +8 sqrt{2} =14sqrt{2}[/latex]