Question

Help my, please...... ​

Answer 1

$\displaystyle 11.~~a)~3\sqrt{18}\cdot(2\sqrt{72}-3\sqrt{288}+5\sqrt{1152}-7\sqrt{648})=\\ \\ =3 \cdot 3\sqrt{2}\cdot(2\cdot6\sqrt{2}-3\cdot12\sqrt{2}+5\cdot24\sqrt{2}-7\cdot18\sqrt{2})=\\ \\=9\sqrt{2}\cdot(12\sqrt{2}-36\sqrt{2}+120\sqrt{2}-126\sqrt{2})=9\sqrt{2}\cdot (-30\sqrt{2})=\mathbf{-540}$

$\displaystyle b)~\sqrt{50}\cdot(4\sqrt{243}-2\sqrt{2028})-\sqrt{8}\cdot(7\sqrt{432}-3\sqrt{3675})=\\ \\ =5\sqrt{2}\cdot(4\cdot9\sqrt{3}-2\cdot26\sqrt{3})-2\sqrt{2}\cdot(7\cdot12\sqrt{3}-3\cdot35\sqrt{3})=\\ \\=5\sqrt{2}\cdot(36\sqrt{3}-52\sqrt{3})-2\sqrt{2}\cdot(84\sqrt{3}-105\sqrt{3})=\\ \\ =5\sqrt{2}\cdot(-16\sqrt{3})-2\sqrt{2}\cdot(-21\sqrt{3})=-80\sqrt{6}\cdo+42\sqrt{6} =\mathbf{-38\sqrt{6}}$

$\displaystyle 12.~~a)~2\sqrt{2}\cdot\sqrt{5}-3\sqrt{5}\cdot\sqrt{2}+4\sqrt{5}\cdot3\sqrt{2}-5\sqrt{5}\cdot4\sqrt{2}=\\ \\=2\sqrt{10}-3\sqrt{10}+12\sqrt{10}-20\sqrt{10}=\mathbf{-9\sqrt{10}}\\ \\ \\ \\b)~\sqrt{21}:\sqrt{7}-5\sqrt{15}:\sqrt{5}+2\cdot3\sqrt{3}-4\sqrt{30}:\sqrt{10}=\\ \\=\sqrt{3}-5\sqrt{3}+6\sqrt{3}-4\sqrt{3}=\mathbf{-2\sqrt{3}}$