$\sqrt{-m^{19}}=\sqrt{-1\ast m^{18}\ast m}=\sqrt{(m^9{)}^2}\ast \sqrt{-m}=|m^9|\ast \sqrt{-m}=-m^9\sqrt{-m}$

$\sqrt{a^{23}{b}^{24}}=\sqrt{a^{22}\ast a\ast (b^{12}{)}^2}=\sqrt{(a^{11}{)}^2}\ast \sqrt{a}\ast \sqrt{(b^{12}{)}^2}=|a^{11}|\ast |b^{12}|\ast \sqrt{a}=a^{11}{b}^{12}\sqrt{a}$, если b ≠ 0

$\sqrt{49a^{2}b}=\sqrt{49\ast a^2\ast b}=\sqrt{7^2}\ast \sqrt{a^2}\ast \sqrt{b}=7\ast |a|\ast \sqrt{b}=-7a\sqrt{b}$, если a < 0

$\sqrt{a^9{b}^9}=\sqrt{a^8\ast a\ast b^8\ast b}=\sqrt{(a^4{)}^2}\ast \sqrt{a}\ast \sqrt{(b^4{)}^2}\ast \sqrt{b}=|a^4|\ast |b^4|\ast \sqrt{ab}=a^4{b}^4\sqrt{ab}$

$\sqrt{27x^{15}{y}^{34}}=\sqrt{9\ast 3\ast x^{14}\ast x\ast (y^{17}{)}^2}=\sqrt{3^2}\ast \sqrt{3}\ast \sqrt{(x^7{)}^2}\ast \sqrt{x}\ast \sqrt{(y^{17}{)}^2}=3\ast |x^7|\ast |y^{17}|\ast \sqrt{3x}=-3x^7{y}^{17}\sqrt{3x}$, если y < 0

$\sqrt{-50m^6{n}^6{p}^7}=\sqrt{-2\ast 25\ast (m^3{)}^2\ast (n^3{)}^2\ast p^6\ast p}=\sqrt{5^2}\ast \sqrt{(m^3{)}^2}\ast \sqrt{(n^3{)}^2}\ast \sqrt{(p^3{)}^2}\ast \sqrt{-2p}=5\ast |m^3|\ast |n^3|\ast |p^3|\ast \sqrt{-2p}=-5m^3{n}^3{p}^3\sqrt{-2p}$, если m > 0, n > 0