Question

2 и 3 задачи для умных

Answer 1

Надеюсь все разберете

См. Фото

Answer 2

$2) \sqrt{31-6\sqrt{26}}-\sqrt{31+6\sqrt{26}}=\\ \\=\sqrt{31-2*3\sqrt{2}\sqrt{13}}-\sqrt{31+2*3\sqrt{2}\sqrt{13}}=\\\\=\sqrt{(3\sqrt{2})^2-2*3\sqrt{2}\sqrt{13}+(\sqrt{13})^2}-\sqrt{(3\sqrt{2})^2+2*3\sqrt{2}\sqrt{13}+(\sqrt{13})^2}=\\\\=\sqrt{(3\sqrt{2}-\sqrt{13})^2}-\sqrt{(3\sqrt{2}+\sqrt{13})^2}=\\\\=3\sqrt{2}-\sqrt{13}-(3\sqrt{2}+\sqrt{13})=\\\\=3\sqrt{2}-\sqrt{13}-3\sqrt{2}-\sqrt{13}=-2\sqrt{13}$

$4)\sqrt[3]{5\sqrt{2}-7}*\sqrt{3+2\sqrt{2}}=\\ \\=\sqrt[3*2]{(5\sqrt{2}-7)^2}*\sqrt[2*3]{(3+2\sqrt{2})^3}=\\\\=\sqrt[6]{(5\sqrt{2})^2-2*5\sqrt{2}*7+7^2}*\sqrt[6]{3^3+3*3^2*2\sqrt{2}+3*3(2\sqrt{2})^2+(2\sqrt{2})^3}=\\\\=\sqrt[6]{50-70\sqrt{2}+49}*\sqrt[6]{27+54\sqrt{2}+72+16\sqrt{2}}=\\\\=\sqrt[6]{99-70\sqrt{2}}*\sqrt[6]{99+70\sqrt{2}}=\\\\=\sqrt[6]{(99-70\sqrt{2})(99+70\sqrt{2})}=\\\\=\sqrt[6]{99^2-(70\sqrt{2})^2}=\sqrt[6]{9801-9800}=\sqrt[6]{1}=1$