Вычеслить: [latex] 5\sqrt{3 \sqrt{32} } -7 \sqrt{15 \sqrt{50} }-4 \sqrt{6 \sqrt{128} } [/latex]

[latex]5\sqrt{3\sqrt{32}}-7\sqrt{15\sqrt{50}}-4\sqrt{6\sqrt{128}}=\\\\=5\sqrt{3\sqrt{16\cdot2}}-7\sqrt{15\sqrt{25\cdot2}}-4\sqrt{6\sqrt{64\cdot 2}}=\\\\=5\sqrt{3\sqrt{4^2\cdot2}}-7\sqrt{15\sqrt{5^2\cdot2}}-4\sqrt{6\sqrt{8^2\cdot 2}}=\\\\=5\sqrt{3\cdot4\sqrt{2}}-7\sqrt{15\cdot5\sqrt{2}}-4\sqrt{6\cdot8\sqrt{2}}=\\\\=5\sqrt{3\cdot4\sqrt{2}}-7\sqrt{3\cdot 5\cdot5\sqrt{2}}-4\sqrt{3\cdot2\cdot8\sqrt{2}}=\\\\=5\sqrt{3\cdot2^2\sqrt{2}}-7\sqrt{3\cdot5^2\sqrt{2}}-4\sqrt{3\cdot4^2\sqrt{2}}=[/latex] [latex]=5\cdot 2\sqrt{3\sqrt{2}}-7\cdot 5\sqrt{3\sqrt{2}}-4\cdot4\sqrt{3\sqrt{2}}=\\\\=10\sqrt{3\sqrt{2}}-35\sqrt{3\sqrt{2}}-16\sqrt{3\sqrt{2}}=-41\sqrt{3\sqrt2}.[/latex]