\[\boxed{\mathbf{535\ (535).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ 4\sqrt{700} - 27\sqrt{7} =\]
\[= 40\sqrt{7} - 27\sqrt{7} = 13\sqrt{7};\]
\[2)\ \sqrt{75} - 6\sqrt{3} = 5\sqrt{3} - 6\sqrt{3} =\]
\[= - \sqrt{3};\]
\[3)\ 2\sqrt{50} - 8\sqrt{2} = 10\sqrt{2} - 8\sqrt{2} =\]
\[= 2\sqrt{2};\]
\[4)\ 5\sqrt{12} - 7\sqrt{3} = 10\sqrt{3} - 7\sqrt{3} =\]
\[= 3\sqrt{3};\]
\[5)\ 3\sqrt{72} - 4\sqrt{2} + 2\sqrt{98} =\]
\[= 18\sqrt{2} - 4\sqrt{2} + 14\sqrt{2} = 28\sqrt{2};\]
\[6)\ \frac{1}{3}\sqrt{108} + \sqrt{363} - \frac{2}{9} \cdot \sqrt{243} =\]
\[= 2\sqrt{3} + 11\sqrt{3} - 2\sqrt{3} = 11\sqrt{3}.\]