Question

80 баллов помогите прошу..................

Answer 1

$\sqrt{11\sqrt{2}-12}+\sqrt{9\sqrt{2}+8}-\sqrt{3\sqrt{2}-4}=\sqrt[4]{2}(\sqrt{11-6\sqrt{2}}+\sqrt{9+4\sqrt{2}}-\sqrt{3-2\sqrt{2}}})=$

$=\sqrt[4]{2}(\sqrt{9-2\sqrt{9\cdot 2}+2}+\sqrt{8+2\sqrt{8\cdot 1}+1}-\sqrt{2-2\sqrt{2\cdot 1}+1}=$

$=\sqrt[4]{2}\left(\sqrt{(3-\sqrt{2})^2}+\sqrt{(\sqrt{8}+1)^2}-\sqrt{(\sqrt{2}-1)^2}\right)=$

$=\sqrt[4]{2}\left(|3-\sqrt{2}|+|2\sqrt{2}+1|-|\sqrt{2}-1|\right)=$

$=\sqrt[4]{2}\left(3-\sqrt{2}+2\sqrt{2}+1-\sqrt{2}+1\right)=5\sqrt[4]{2}$