$\sqrt{10a^2}=\sqrt{10}\ast \sqrt{a^2}=\sqrt{10}\ast |a|=a\sqrt{10}$, если a ≥ 0

$\sqrt{15b^2}=\sqrt{15\ast b^2}=\sqrt{15}\ast |b|=-b\sqrt{15}$, если b ≤ 0

$\sqrt{x^{11}{y}^{12}}=\sqrt{x\ast x^{10}\ast (y^6{)}^2}=\sqrt{x}\ast \sqrt{(x^5{)}^2}\ast \sqrt{(y^6{)}^2}=\sqrt{x}\ast |x^5|\ast |y^6|=x^5{y}^6\sqrt{x}$, если y ≠ 0

$\sqrt{36m^{2}n}=\sqrt{36}\ast \sqrt{m^2}\ast \sqrt{n}=6|m|\ast \sqrt{n}=-6m\sqrt{n}$, если m < 0

$\sqrt{4x^6{y}^5}=\sqrt{4}\ast \sqrt{x^6}\ast \sqrt{y^5}=2\ast \sqrt{(x^3{)}^2}\ast \sqrt{y^4\ast y}=2\ast |x^3|\ast \sqrt{(y^2{)}^2\ast y}=2x^3{y}^2\sqrt{y}$, если x > 0

$\sqrt{700a^5{b}^{2}2}=\sqrt{700}\ast \sqrt{a^5}\ast \sqrt{b^{2}2}=\sqrt{100\ast 7}\ast \sqrt{a^{4}a}\ast \sqrt{(b^{11}{)}^2}=10\sqrt{7}\ast \sqrt{(a^2{)}^2\ast a}\ast |b^{11}|=-10\sqrt{7}\ast a^2\sqrt{a}{b}^{11}=-10a^2{b}^{11}\sqrt{7a}$, если b < 0