Đáp án:
\(\begin{array}{l}
a)\dfrac{3}{{25}}\\
b)\dfrac{{3\sqrt {21} }}{{10}}\\
c)\dfrac{3}{{20}}\\
d)2a\\
e) - \dfrac{2}{3}\\
f)\dfrac{1}{{126}}\\
g)x\sqrt x .{y^2}\sqrt y \\
h)\dfrac{{{c^2}d\sqrt {cd} }}{3}\\
i)\dfrac{1}{{x\sqrt x .y\sqrt y }}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\sqrt {\dfrac{{144}}{{1000}}:10} = \dfrac{3}{{25}}\\
b)\sqrt {\dfrac{{1890}}{{1000}}} = \dfrac{{3\sqrt {21} }}{{10}}\\
c)\sqrt {\dfrac{{225}}{{1000}}} :\sqrt {10} = \dfrac{{3\sqrt {10} }}{{20}}.\dfrac{1}{{\sqrt {10} }} = \dfrac{3}{{20}}\\
d)\dfrac{{2a\sqrt {2ab} }}{{\sqrt {2ab} }} = 2a\\
e)\left( {3\sqrt 6 - 5\sqrt 6 } \right):3\sqrt 6 \\
= \left( { - 2\sqrt 6 } \right):3\sqrt 6 \\
= - \dfrac{2}{3}\\
f)\dfrac{{\sqrt {15} }}{3}:42\sqrt {15} \\
= \dfrac{1}{{3.42}} = \dfrac{1}{{126}}\\
g)x\sqrt y .xy\sqrt {xy} .\dfrac{{\sqrt y }}{{\sqrt x }}\\
= {x^2}{y^2}.\dfrac{{\sqrt y }}{{\sqrt x }}\\
= x\sqrt x .{y^2}\sqrt y \\
h)c.\sqrt {\dfrac{d}{3}} :\dfrac{{\sqrt 3 }}{{cd\sqrt c }}\\
= c.\sqrt {\dfrac{d}{3}} .\dfrac{{cd\sqrt c }}{{\sqrt 3 }}\\
= \dfrac{{{c^2}d\sqrt {cd} }}{3}\\
i)\dfrac{x}{y}\sqrt {xy} .\dfrac{y}{x}.\sqrt x .\dfrac{1}{{xy.x.y\sqrt x }}\\
= \dfrac{{x\sqrt y }}{{{x^2}{y^2}\sqrt x }}\\
= \dfrac{1}{{x\sqrt x .y\sqrt y }}
\end{array}\)
