Đáp án:
\(\begin{array}{l}
a)\dfrac{5}{6}\\
b)14\sqrt 3 \\
c)4\\
d)3
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)A = \sqrt {\dfrac{{25}}{8}} .\sqrt {\dfrac{2}{9}} = \dfrac{{5\sqrt 2 }}{{2\sqrt 2 .3}} = \dfrac{5}{6}\\
b)B = \dfrac{1}{3}.3\sqrt 3 - 3.4\sqrt 3 + 5.5\sqrt 3 \\
= \left( {1 - 12 + 25} \right)\sqrt 3 = 14\sqrt 3 \\
c)C = \left( {5\sqrt 2 - 4\sqrt 2 + 3\sqrt 2 } \right):\sqrt 2 \\
= \dfrac{{4\sqrt 2 }}{{\sqrt 2 }} = 4\\
d)D = \dfrac{{\sqrt 3 \left( {\sqrt 3 - 2} \right)}}{{\sqrt 3 - 2}} + \sqrt {9 + 2.3.\sqrt 3 + 3} - 2\sqrt 3 \\
= \sqrt 3 + \sqrt {{{\left( {3 + \sqrt 3 } \right)}^2}} - 2\sqrt 3 \\
= - \sqrt 3 + 3 + \sqrt 3 = 3
\end{array}\)
