Question

Задание смотреть на картинке

Answer 1

$1)\; \; x\geq 0:\; \sqrt{11x^2}=\sqrt{11}\cdot |x|=x\sqrt{11}\\\\2)\; \; y\leq 0:\; \sqrt{13y^2}=\sqrt{13}\cdot |y|=-y\sqrt{13}\\\\3)\; \; \sqrt{20c^{12}}=\sqrt{20}\cdot |c^6|=c^6\cdot 2\sqrt5\\\\4)\; \; \sqrt{x^{17}}=\sqrt{x^{16}\cdot x}=|x^8|\cdot \sqrt{x}=x^8\cdot \sqrt{x}\\\\5)\; \; \sqrt{-c^{15}}=\sqrt{-c^{14}\cdot c}=|c^7|\cdot \sqrt{-c}=\Big [\; -c\geq 0\; \; \to \; \; c\leq 0\; \Big ]=-c^7\cdot \sqrt{-c}$

$6)\; \; m\ne 0:\; \sqrt{m^{16}\, n^3}=\sqrt{(m^8)^2\cdot n^2\cdot n}=|m^8|\cdot |n|\cdot \sqrt{n}=\\\\=\Big [\; n\geq 0\; \Big ]=m^8\, n\sqrt{n}\\\\7)\; \; c<0:\; \sqrt{49bc^2}=7\cdot |c|\sqrt{b}=-7\, c\sqrt{b} \\\\8)\; \; x\leq 0\; ,\; y\leq 0:\; \sqrt{x^{11}\, y^{11}}=\sqrt{x^{10}\cdot x\cdot y^{10}\cdot y}=|x^5|\cdot |y^5|\cdot \sqrt{xy}=\\\\=(-x^5)\cdot (-y^5)\cdot \sqrt{xy}=x^5y^5\sqrt{xy}$

$9)\; \; y>0:\; \sqrt{64x^7y^{26}}=8\cdot \sqrt{x^6\cdot x\cdot (y^{13})^2}=8\cdot |x^3|\cdot |y^{13}|\cdot \sqrt{x}=\\\\=\Big [\; x\geq 0\; \Big ]=8\, x^3\cdot y^{13}\cdot \sqrt{x}\\\\10)\; \; m<0:\; \sqrt{700\, m^{18}n^{19}}=\sqrt{100\cdot 7\cdot (m^9)^2\cdot n^{18}\cdot n}=\\\\=10\cdot |m^9|\cdot |n^9|\cdot \sqrt{7n}=\Big [\; n\geq 0\; \Big ]=10\cdot (-m^9)\cdot n^9\cdot \sqrt{7n}=\\\\=-10\, m^9\, n^9\cdot \sqrt{7n}$