Đưa thừa số ra ngoài dấu căn:

\(a)\,\,\,\sqrt {180{x^2}} \\ b)\,\sqrt {3{x^2} - 6xy + 3{y^2}} \)
A.\(\begin{array}{l}a)\,\,6x\sqrt 5 \\b)\,\,\,\left\{ \begin{array}{l}\left( {x - y} \right)\sqrt 3 \,\,\,\,khi\,\,\,\,x \ge y\\\left( {y - x} \right)\sqrt x \,\,\,\,khi\,\,\,x < y\end{array} \right..\end{array}\)
B.\(\begin{array}{l}a)\,\,\, - 6x\sqrt 5 \\b)\,\,\left( {x - y} \right)\sqrt 3 \end{array}\)
C.\(\begin{array}{l}a)\,\,\left\{ \begin{array}{l}6x\sqrt 5 \,\,\,khi\,\,\,x \ge 0\\ - 6x\sqrt 5 \,\,\,\,khi\,\,\,x < 0\end{array} \right.\\b)\,\,\,\left\{ \begin{array}{l}\left( {x - y} \right)\sqrt 3 \,\,\,khi\,\,\,x \ge 0\\\left( {y - x} \right)\sqrt 3 \,\,\,khi\,\,\,x < y\end{array} \right..\end{array}\)
D.\(\begin{array}{l}a)\,\, - 6x\sqrt 5 \\b)\,\, - \left( {x - y} \right)\sqrt 3 \end{array}\)

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Đưa thừa số vào trong dấu căn

\(\begin{array}{l}a)\,\,\frac{1}{{xy}}\sqrt {\frac{{{x^2}{y^2}}}{2}}  &  &  & b)\,\,a\sqrt 2  &  &  & c)\,\, - \frac{a}{b}\sqrt {\frac{b}{a}} \,\,\,\left( {a > 0,\,\,\,b > 0} \right)\\d)\,\,a\sqrt {\frac{3}{a}}  &  &  & e)\,\,\frac{1}{{2x - 1}}\sqrt {5\left( {1 - 4x + 4{x^2}} \right)} .\end{array}\)
A.\(\begin{array}{l}a)\,\,\left\{ \begin{array}{l}\frac{{\sqrt 2 }}{2}\,\,\,khi\,\,\,xy > 0\\ - \frac{{\sqrt 2 }}{2}\,\,\,khi\,\,\,xy < 0\end{array} \right.\\b)\,\,\left\{ \begin{array}{l}\sqrt {2{a^2}} \,\,\,\,khi\,\,\,a \ge 0\\ - \sqrt {2{a^2}} \,\,\,\,khi\,\,\,a \frac{1}{2}\\ - \sqrt 5 \,\,\,khi\,\,\,x < \frac{1}{2}\end{array} \right.\end{array}\)
B.\(\begin{array}{l}a)\,\,\left\{ \begin{array}{l}\frac{{\sqrt 2 }}{2}\,\,\,khi\,\,\,xy > 0\\ - \frac{{\sqrt 2 }}{2}\,\,\,khi\,\,\,xy < 0\end{array} \right.\\b)\,\,\left\{ \begin{array}{l}\sqrt {2{a^2}} \,\,\,\,khi\,\,\,a \ge 0\\ - \sqrt {2{a^2}} \,\,\,\,khi\,\,\,a < 0\end{array} \right.\\c)\,\, - \sqrt {\frac{a}{b}} \\d)\,\,\left\{ \begin{array}{l}\sqrt 5 \,\,\,khi\,\,\,x \ge \frac{1}{2}\\ - \sqrt 5 \,\,\,khi\,\,\,x < \frac{1}{2}\end{array} \right.\end{array}\)
C.\(\begin{array}{l}a)\,\,\frac{{\sqrt 2 }}{2}\\b)\,\,\left\{ \begin{array}{l}\sqrt {2{a^2}} \,\,\,\,khi\,\,\,a \ge 0\\ - \sqrt {2{a^2}} \,\,\,\,khi\,\,\,a < 0\end{array} \right.\\c)\,\,\sqrt {\frac{a}{b}} \\d)\,\,\left\{ \begin{array}{l}\sqrt 5 \,\,\,khi\,\,\,x \ge \frac{1}{2}\\ - \sqrt 5 \,\,\,khi\,\,\,x < \frac{1}{2}\end{array} \right.\end{array}\)
D.\(\begin{array}{l}a)\,\,\frac{{\sqrt 2 }}{2}\\b)\,\,\left\{ \begin{array}{l}\sqrt {2{a^2}} \,\,\,\,khi\,\,\,a \ge 0\\ - \sqrt {2{a^2}} \,\,\,\,khi\,\,\,a < 0\end{array} \right.\\c)\,\,\sqrt {\frac{a}{b}} \\d)\,\,\sqrt 5 \end{array}\)