Question

пожалуйста помогите​

Answer 1

$\sqrt{26-8\sqrt{2+\sqrt{9+\sqrt{32}}}}=\sqrt{26-8\sqrt{2+\sqrt{(\sqrt{8}+1)^2}}}=\\ \\ \\ =\sqrt{26-8\sqrt{2+|\sqrt{8}+1|}}=\sqrt{26-8\sqrt{2+\sqrt{8}+1}}=\sqrt{26-8\sqrt{3+\sqrt{8}}}=\\ \\ \\ =\sqrt{26-8\sqrt{(\sqrt{2}+1)^2}}=\sqrt{26-8|\sqrt{2}+1|}=\sqrt{26-8(\sqrt{2}+1)}=\\ \\ \\ =\sqrt{26-8\sqrt{2}-8}=\sqrt{18-8\sqrt{2}}=\sqrt{(4-\sqrt{2})^2}=|4-\sqrt{2}|=4-\sqrt{2}$