Question

ДАЮ 60 БАЛЛОВ КАК МОЖНО БОЛЕЕ ПОДРОБНО, СПАСИБО√(26-8√(2+√(9+√32)))

Answer 1

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

Ответ: $4-\sqrt{2}.$