Đáp án:
$\begin{array}{l}
a)\dfrac{{ - 17\sqrt 3 }}{3}\\
b)0\\
c)\left( {16\sqrt 2 - 2a} \right).\sqrt a
\end{array}$
Giải thích bước giải:
$\begin{array}{l}
a)\dfrac{1}{2}\sqrt {48} - 2\sqrt {75} - \dfrac{{\sqrt {33} }}{{\sqrt {11} }} + 5\sqrt {1\dfrac{1}{3}} \\
= \dfrac{1}{2}.4\sqrt 3 - 2.5\sqrt 3 - \dfrac{{\sqrt {11} .\sqrt 3 }}{{\sqrt {11} }} + 5.\sqrt {\dfrac{4}{3}} \\
= 2\sqrt 3 - 10\sqrt 3 - \sqrt 3 + 5.\dfrac{{2\sqrt 3 }}{3}\\
= - 9\sqrt 3 + \dfrac{{10\sqrt 3 }}{3}\\
= \dfrac{{ - 17\sqrt 3 }}{3}\\
b)\sqrt {6 + 2\sqrt 5 } - \sqrt {6 - 2\sqrt 5 } - \sqrt[3]{8}\\
= \sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} - \sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} - 2\\
= \sqrt 5 + 1 - \sqrt 5 + 1 - 2\\
= 0\\
c)5\sqrt {2a} - \sqrt {50a} - 2\sqrt {{a^3}} + 4\sqrt {32a} \\
= 5\sqrt {2a} - 5\sqrt {2a} - 2.a.\sqrt a + 4.4\sqrt {2a} \\
= \left( {16\sqrt 2 - 2a} \right).\sqrt a
\end{array}$
