0\; ,\; b<0\\\\\sqrt{9a^3b^6}=\sqrt{3^2\cdot a^2\cdot a\cdot (b^3)^2}=3\cdot |a|\cdot |b^3|\cdot \sqrt{a}=3a|b|^3\cdot \sqrt{a}=\\\\=3a\cdot (-b)^3\cdot \sqrt{a}=-3ab^3\cdot\sqrt{a}\\\\2)\; \; m>0\; ,\; \; n<0\\\\\sqrt{0,25m^3n^6}=\sqrt{(0,5)^2\cdot m^2\cdot m\cdot (n^3)^2}=0,5\cdot |m|\cdot |n^3|\cdot \sqrt{m}=\\\\=0,5\cdot m\cdot (-n^3)\cdot \sqrt{m}=-0,5mn^3\cdot \sqrt{m}" alt="\star \; \; \sqrt{x^2}=|x|=\left \{ {{x\; ,\; esli\; x\geq 0\; ,} \atop {-x\; ,\; esli\; x<0\; .}} \right. \; \; \star \\\\\\1)\; \; a>0\; ,\; b<0\\\\\sqrt{9a^3b^6}=\sqrt{3^2\cdot a^2\cdot a\cdot (b^3)^2}=3\cdot |a|\cdot |b^3|\cdot \sqrt{a}=3a|b|^3\cdot \sqrt{a}=\\\\=3a\cdot (-b)^3\cdot \sqrt{a}=-3ab^3\cdot\sqrt{a}\\\\2)\; \; m>0\; ,\; \; n<0\\\\\sqrt{0,25m^3n^6}=\sqrt{(0,5)^2\cdot m^2\cdot m\cdot (n^3)^2}=0,5\cdot |m|\cdot |n^3|\cdot \sqrt{m}=\\\\=0,5\cdot m\cdot (-n^3)\cdot \sqrt{m}=-0,5mn^3\cdot \sqrt{m}" align="absmiddle" class="latex-formula">
0\; ,\; \; d<0\\\\\sqrt{0,01c^3d^2}=\sqrt{(0,1)^2\cdot c^2\cdot c\cdot d^2}=0,1\cdot |c|\cdot |d|\cdot \sqrt{c}=\\\\=0,1\cdot c\cdot (-d)\cdot \sqrt{c}=-0,1\, c\, d\cdot \sqrt{c}\\\\4)\; \; a<0\; ,\; \; m>0\\\\\sqrt{36\, a^2\, m^5}=\sqrt{6^2\cdot a^2\cdot m^4\cdot m}=6\cdot |a|\cdot \sqrt{(m^2)^2\cdot m}=\\\\=6\cdot (-a)\cdot |\underbrace {m^2}_{\geq 0}|\cdot \sqrt{m}=-6a\cdot m^2\cdot \sqrt{m}" alt="3)\; \; c>0\; ,\; \; d<0\\\\\sqrt{0,01c^3d^2}=\sqrt{(0,1)^2\cdot c^2\cdot c\cdot d^2}=0,1\cdot |c|\cdot |d|\cdot \sqrt{c}=\\\\=0,1\cdot c\cdot (-d)\cdot \sqrt{c}=-0,1\, c\, d\cdot \sqrt{c}\\\\4)\; \; a<0\; ,\; \; m>0\\\\\sqrt{36\, a^2\, m^5}=\sqrt{6^2\cdot a^2\cdot m^4\cdot m}=6\cdot |a|\cdot \sqrt{(m^2)^2\cdot m}=\\\\=6\cdot (-a)\cdot |\underbrace {m^2}_{\geq 0}|\cdot \sqrt{m}=-6a\cdot m^2\cdot \sqrt{m}" align="absmiddle" class="latex-formula">