$\sqrt{-m^9}=\sqrt{(-m{)}^8\ast (-m)}=|-m{|}^4\ast \sqrt{-m}=m^4\sqrt{-m}$

$\sqrt{a^4{b}^{13}}=\sqrt{a^4\ast b^{12}\ast b}=\sqrt{(a^2{)}^2}\ast \sqrt{(b^6{)}^2}\ast \sqrt{b}=a^2{b}^6\sqrt{b}$, если a ≠ 0

$\sqrt{4x^{6}y}=\sqrt{4\ast (x^3{)}^2\ast y}=\sqrt{2^2}\ast \sqrt{(x^3{)}^2}\ast \sqrt{y}=2\ast |x^3|\ast \sqrt{y}=-2x^3\sqrt{y}$, если x < 0

$\sqrt{m^7{n}^7}=\sqrt{m^6\ast m\ast n^6\ast n}=\sqrt{(m^3{)}^2}\ast \sqrt{m}\ast \sqrt{(n^3{)}^2}\ast \sqrt{n}=|m^3|\ast |n^3|\ast \sqrt{mn}=m^3{n}^3\sqrt{mn}$, если m ≤ 0, n ≤ 0

$\sqrt{45x^3{y}^{14}}=\sqrt{9\ast 5\ast x^2\ast x\ast (y^7{)}^2}=\sqrt{3^2}\ast \sqrt{5}\ast \sqrt{x^2}\ast \sqrt{x}\ast \sqrt{(y^7{)}^2}=3\ast |y^7|\ast \sqrt{5x}=-3y^7\sqrt{5x}$, если y < 0

$\sqrt{64a^2{b}^9}=\sqrt{8^2\ast a^2\ast b^8\ast b}=\sqrt{8^2}\ast \sqrt{a^2}\ast \sqrt{(b^4{)}^2}\ast \sqrt{b}=8\ast |a|\ast |b^4|\ast \sqrt{b}=8a{b}^4\sqrt{b}$, если a > 0

$\sqrt{242m^{11}{b}^{18}}=\sqrt{2\ast 121\ast m^{10}\ast m\ast (b^9{)}^2}=\sqrt{2}\ast \sqrt{{11}^2}\ast \sqrt{(m^5{)}^2}\ast \sqrt{m}\ast \sqrt{(b^9{)}^2}=11\ast |m^5|\ast |b^9|\ast \sqrt{2m}=-11m^5{b}^9\sqrt{2m}$, если b < 0

$\sqrt{-m^2{n}^2{p}^{15}}=\sqrt{-1\ast m^2\ast n^2\ast p^{14}\ast p}=\sqrt{m^2}\ast \sqrt{n^2}\ast \sqrt{(p^7{)}^2}\ast \sqrt{-p}=|m^2|\ast |n^2|\ast |p^7|\ast \sqrt{-p}=m^2{n}^2{p}^7\sqrt{-p}$, если m > 0, n < 0