Докажите тождества: [latex]1)\quad ( \sqrt[6]{5+2\sqrt6}+\sqrt[3]{\sqrt3+\sqrt2})*\sqrt[3]{\sqrt2-\sqrt3}=0;\\ 2)\quad \sqrt{20,25}+\sqrt[3]{24}-\sqrt[4]{0,1296}-\frac{2}{5}\sqrt[3]{375}+\frac{1}{3} \sqrt[5]{7\frac{19}{32}}=4,4...

[latex] (\sqrt[6]{5+2\sqrt6} +\sqrt[3]{\sqrt3+\sqrt2})\cdot \sqrt[3]{\sqrt2-\sqrt3}=\\\\=[\, (\sqrt3+\sqrt2)^2=3+2\sqrt2\cdot \sqrt3+3=5+2\sqrt6\, ]=\\\\=(\sqrt[6]{(\sqrt3+\sqrt2)^2}+\sqrt[3]{\sqrt3+\sqrt2})\cdot \sqrt[3]{\sqrt2-\sqrt3}=\\\\=(\sqrt[3]{\sqrt3+\sqrt2}+\sqrt[3]{\sqrt3+\sqrt2}\, )\cdot \sqrt[3]{\sqrt2-\sqrt3}=\\\\=2\sqrt[3]{\sqrt3+\sqrt2}\cdot \sqrt[3]{\sqrt2-\sqrt3}=2\cdot \sqrt[3]{(\sqrt2+\sqrt3)(\sqrt2-\sqrt3)}=\\\\=2\cdot \sqrt[3]{2-3}=-2[/latex] [latex]2)\; \; \sqrt{20,25}+\sqrt[3]{24}-\sqrt[4]{0,1296}-\frac{2}{5}\sqrt[3]{375}+\frac{1}{3}\sqrt[5]{7\frac{19}{32}}=\\\\=\sqrt{\frac{81}{4}}+\sqrt[3]{8\cdot 3}-\sqrt[4]{\frac{1296}{10000}}-\frac{2}{5}\sqrt[3]{125\cdot 3}+\frac{1}{3}\sqrt[5]{\frac{243}{32}}=\\\\=\frac{9}{2}+2\sqrt3-\frac{6}{10}-\frac{2}{5}\cdot 5\sqrt3+\frac{1}{3}\cdot \frac{3}{2}=\\\\=\frac{9}{2}+2\sqrt3-\frac{3}{5}-2\sqrt3+\frac{1}{2}=5-\frac{3}{5}=\frac{25-3}{5}=\frac{22}{5}=4,4[/latex]