[tex]\displaystyle\bf\\1)\\\\\sqrt{7m^{2} } =m\sqrt{7} \\\\2)\\\\\sqrt{14x^{2} } =-x\sqrt{14}\\\\3)\\\\\sqrt{125x^{12} } =\sqrt{25\cdot 5\cdot(x^{6} )^{2} } =5x^{6} \sqrt{5} \\\\4)\\\\\sqrt{-y^{3} } =\sqrt{-y^{2} \cdot y} =|y|\sqrt{-y} \\\\\\1)\\\\0,8\sqrt{225} +0,6\sqrt{1,44} =0,8\sqrt{15^{2} } +0,6\sqrt{1,2^{2} } =0,8\cdot 15+0,6\cdot 1,2=\\\\=12+0,72=12,72[/tex]
[tex]\displaystyle\bf\\2)\\\\(2\sqrt{3} )^{2} -(3\sqrt{2} )^{2} =4\cdot 3-9\cdot 2=12-18=-6[/tex]
[tex]\displaystyle\bf\\3)\\\\\sqrt{3^{4} \cdot2^{6} } =\sqrt{(3^{2})^{2} \cdot (2^{3} )^{2} } =3^{2} \cdot 2^{3} =9\cdot 8=72\\\\4)\\\\\sqrt{32} \cdot \sqrt{2} -\frac{\sqrt{28} }{\sqrt{7} } =\sqrt{16\cdot 2\cdot 2} -\sqrt{\frac{7\cdot 4}{7} } =\sqrt{4^{2} \cdot2^{2} } -\sqrt{4} =\\\\=4\cdot 2-2=8-2=6[/tex]
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Answers & Comments
[tex]\displaystyle\bf\\1)\\\\\sqrt{7m^{2} } =m\sqrt{7} \\\\2)\\\\\sqrt{14x^{2} } =-x\sqrt{14}\\\\3)\\\\\sqrt{125x^{12} } =\sqrt{25\cdot 5\cdot(x^{6} )^{2} } =5x^{6} \sqrt{5} \\\\4)\\\\\sqrt{-y^{3} } =\sqrt{-y^{2} \cdot y} =|y|\sqrt{-y} \\\\\\1)\\\\0,8\sqrt{225} +0,6\sqrt{1,44} =0,8\sqrt{15^{2} } +0,6\sqrt{1,2^{2} } =0,8\cdot 15+0,6\cdot 1,2=\\\\=12+0,72=12,72[/tex]
[tex]\displaystyle\bf\\2)\\\\(2\sqrt{3} )^{2} -(3\sqrt{2} )^{2} =4\cdot 3-9\cdot 2=12-18=-6[/tex]
[tex]\displaystyle\bf\\3)\\\\\sqrt{3^{4} \cdot2^{6} } =\sqrt{(3^{2})^{2} \cdot (2^{3} )^{2} } =3^{2} \cdot 2^{3} =9\cdot 8=72\\\\4)\\\\\sqrt{32} \cdot \sqrt{2} -\frac{\sqrt{28} }{\sqrt{7} } =\sqrt{16\cdot 2\cdot 2} -\sqrt{\frac{7\cdot 4}{7} } =\sqrt{4^{2} \cdot2^{2} } -\sqrt{4} =\\\\=4\cdot 2-2=8-2=6[/tex]