Đáp án: $\sqrt{6+2\sqrt{14-2\sqrt[4]{2}+4\sqrt{3}-2\sqrt{2}}}$
Giải thích các bước giải:
$\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\sqrt{2}}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}\\=\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt[4]{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}\\=\sqrt{6+2\sqrt{2(3-\sqrt[4]{2}+\sqrt{12}+\sqrt{18-\sqrt{128}})}}\\=\sqrt{6+2\sqrt{2(3-\sqrt[4]{2}+2\sqrt{3}+\sqrt{18-8\sqrt{2}})}}\\=\sqrt{6+2\sqrt{2(3-\sqrt[4]{2}+2\sqrt{3}+\sqrt{(4-\sqrt{2})^{2}})}}\\=\sqrt{6+2\sqrt{2(3-\sqrt[4]{2}+2\sqrt{3}+4-\sqrt{2})}}\\=\sqrt{6+2\sqrt{2(7-\sqrt[4]{2}+2\sqrt{3}-\sqrt{2})}}\\=\sqrt{6+2\sqrt{14-2\sqrt[4]{2}+4\sqrt{3}-2\sqrt{2}}}$
