by 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 \(\begin{array}{l}
a)\,\, – 6x\sqrt 5 \\
b)\,\, – \left( {x – y} \right)\sqrt 3
\end{array}\)
Hướng dẫn Chọn đáp án là: C
Lời giải chi tiết:
\(\begin{array}{l}a)\,\,\,\sqrt {180{x^2}} = \sqrt {36.5{x^2}} = 6\left| x \right|\sqrt 5 = \left\{ \begin{array}{l}6x\sqrt 5 \,\,\,\,\,khi\,\,\,x \ge 0\\ – 5x\sqrt 5 \,\,\,\,\,khi\,\,\,x < 0\end{array} \right..\\b)\,\,\,\sqrt {3{x^2} – 6xy + 3{y^2}} = \sqrt {3\left( {{x^2} – 2xy + {y^2}} \right)} = \sqrt {3{{\left( {x – y} \right)}^2}} \\ = \sqrt 3 \left| {x – y} \right| = \left\{ \begin{array}{l}\sqrt 3 \left( {x – y} \right)\,\,\,\,\,khi\,\,\,x \ge y\\ – \sqrt 3 \left( {x – y} \right)\,\,\,\,\,khi\,\,\,\,x < y\end{array} \right..\end{array}\)
