Đáp án:
\(\begin{array}{l}
a)\dfrac{{\sqrt {10} }}{{15}}\\
b)\dfrac{{2\sqrt 5 - \sqrt {15} }}{{25}}\\
c)\dfrac{{\sqrt {10} }}{{14}}\\
d)\dfrac{{\sqrt {3x} }}{x}\\
e)\dfrac{{x\sqrt {5xy} }}{{7y}}\\
f) - 7\sqrt { - 3xy}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\sqrt {\dfrac{{12}}{{270}}} = \dfrac{{\sqrt {10} }}{{15}}\\
b)\sqrt {\dfrac{{{{\left( {2 - \sqrt 3 } \right)}^2}}}{{75}}} = \dfrac{{2 - \sqrt 3 }}{{5\sqrt 5 }} = \dfrac{{2\sqrt 5 - \sqrt {15} }}{{25}}\\
c)\sqrt {\dfrac{5}{{98}}} = \dfrac{{\sqrt 5 }}{{7\sqrt 2 }} = \dfrac{{\sqrt {10} }}{{14}}\\
d)\sqrt {\dfrac{3}{x}} = \dfrac{{\sqrt 3 }}{{\sqrt x }} = \dfrac{{\sqrt {3x} }}{x}\\
e)\sqrt {\dfrac{{5{x^3}}}{{49y}}} = \dfrac{{x\sqrt {5x} }}{{7\sqrt y }} = \dfrac{{x\sqrt {5xy} }}{{7y}}\\
f)7xy.\sqrt {\dfrac{{ - 3}}{{xy}}} = 7xy.\dfrac{{\sqrt { - 3xy} }}{{\left| {xy} \right|}}\\
= 7xy.\left( { - \dfrac{{\sqrt { - 3xy} }}{{xy}}} \right)\\
= - 7\sqrt { - 3xy}
\end{array}\)
