$\sqrt{q^2}=|q|=q$, если q > 0

$\sqrt{t^2}=|t|=-<!--\; -\; -->t$, если t ≤ 0

$\sqrt{49m^2{n}^8}=\sqrt{7^2{m}^2(n^4{)}^2}=|7m{n}^4|=7m{n}^4$, если m ≥ 0

$\sqrt{0,81a^6{b}^{10}}=\sqrt{0,9^2(a^3{)}^2(b^5{)}^2}=|0,9a^3{b}^5|=-<!--\; -\; -->0,9a^3{b}^5$, если a ≥ 0, b ≤ 0

$\frac{1}{5}x\sqrt{100x^{26}}=\frac{1}{5}x\sqrt{{10}^2(x^{13}{)}^2}=\frac{1}{5}x\ast <!--\; \ast \; -->|10x^{13}|=\frac{1}{5}x\ast <!--\; \ast \; -->(-<!--\; -\; -->10x^{13})=-<!--\; -\; -->2x^{14}$, если x ≤ 0

$\frac{\sqrt{a^6{b}^{20}{c}^{34}}}{a{b}^8{c}^{12}}=\frac{\sqrt{(a^3{)}^2(b^{10}{)}^2(c^{17}{)}^2}}{a{b}^8{c}^{12}}=\frac{|a^3{b}^{10}{c}^{17}|}{a{b}^8{c}^{12}}=\frac{-<!--\; -\; -->a^3{b}^{10}{c}^{17}}{a{b}^8{c}^{12}}=-<!--\; -\; -->a^2{b}^2{c}^5$, если a > 0, c < 0

$\frac{1,2x^3}{y^5}\sqrt{\frac{y^{14}}{x^{10}}}=\frac{1,2x^3}{y^5}\ast <!--\; \ast \; -->\frac{\sqrt{y^{14}}}{\sqrt{x^{10}}}=\frac{1,2x^3}{y^5}\ast <!--\; \ast \; -->\frac{\sqrt{(y^7{)}^2}}{\sqrt{(x^5{)}^2}}=\frac{1,2x^3}{y^5}\ast <!--\; \ast \; -->\frac{|y^7|}{|x^5|}=\frac{1,2x^3}{y^5}\ast <!--\; \ast \; -->(-<!--\; -\; -->\frac{y^7}{x^5})=\frac{1,2}{1}\ast <!--\; \ast \; -->(-<!--\; -\; -->\frac{y^2}{x^2})=-<!--\; -\; -->\frac{1,2y^2}{x^2}$, если y > 0, x < 0

$-<!--\; -\; -->0,1x^2\sqrt{1,96x^{18}{y}^{16}}=-<!--\; -\; -->0,1x^2\sqrt{1,4^2(x^9{)}^2(y^8{)}^2}=-<!--\; -\; -->0,1x^2\ast <!--\; \ast \; -->|1,4x^9{y}^8|=-<!--\; -\; -->0,1x^2\ast <!--\; \ast \; -->(-<!--\; -\; -->1,4x^9{y}^8)=0,14x^{11}{y}^8$, если x ≤ 0