Câu hỏi:
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 \(\begin{array}{l}
a)\,\, - 6x\sqrt 5 \\
b)\,\, - \left( {x - y} \right)\sqrt 3
\end{array}\)
Phương pháp giải:
Lời giải chi tiết:
\(\begin{array}{l}a)\,\,\,\sqrt {180{x^2}} = \sqrt {36.5{x^2}} = 6\left| x \right|\sqrt 5 = \left\{ \begin{array}{l}6x\sqrt 5 \,\,\,\,\,khi\,\,\,x \ge 0\\ - 5x\sqrt 5 \,\,\,\,\,khi\,\,\,x < 0\end{array} \right..\\b)\,\,\,\sqrt {3{x^2} - 6xy + 3{y^2}} = \sqrt {3\left( {{x^2} - 2xy + {y^2}} \right)} = \sqrt {3{{\left( {x - y} \right)}^2}} \\ = \sqrt 3 \left| {x - y} \right| = \left\{ \begin{array}{l}\sqrt 3 \left( {x - y} \right)\,\,\,\,\,khi\,\,\,x \ge y\\ - \sqrt 3 \left( {x - y} \right)\,\,\,\,\,khi\,\,\,\,x < y\end{array} \right..\end{array}\)
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