Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
b,\\
2\sqrt {8\sqrt 3 } - 2\sqrt {5\sqrt 3 } - 3\sqrt {20\sqrt 3 } \\
= 2\sqrt {{2^2}.2.\sqrt 3 } - 2.\sqrt {5\sqrt 3 } - 3.\sqrt {{2^2}.5\sqrt 3 } \\
= 2.2.\sqrt {2\sqrt 3 } - 2.\sqrt {5\sqrt 3 } - 3.2.\sqrt {5\sqrt 3 } \\
= 4\sqrt {2\sqrt 3 } - 2\sqrt {5\sqrt 3 } - 6\sqrt {5\sqrt 3 } \\
= 4\sqrt {2\sqrt 3 } - 8\sqrt {5\sqrt 3 } \\
= 4\sqrt 2 .\sqrt {\sqrt 3 } - 8\sqrt 5 .\sqrt {\sqrt 3 } \\
= 4\sqrt {\sqrt 3 } .\left( {\sqrt 2 - 2\sqrt 5 } \right)\\
c,\\
\dfrac{2}{{2a - 1}}.\sqrt {5{a^2}.\left( {1 - 4a + 4{a^2}} \right)} \\
= \dfrac{1}{{2a - 1}}.\sqrt {5{a^2}.{{\left( {2a - 1} \right)}^2}} \\
= \dfrac{1}{{2a - 1}}.\left| {\sqrt 5 a.\left( {2a - 1} \right)} \right|\\
= \dfrac{1}{{2a - 1}}.\sqrt 5 .a.\left( {2a - 1} \right)\,\,\,\,\,\,\,\,\,\left( {a > 0,5} \right)\\
= \sqrt 5 a\\
d,\\
\dfrac{2}{{{x^2} - {y^2}}}.\sqrt {\dfrac{{3{{\left( {x + y} \right)}^2}}}{2}} \\
= \dfrac{2}{{\left( {x - y} \right)\left( {x + y} \right)}}.\sqrt {\dfrac{3}{2}} .\left| {x + y} \right|\\
= \dfrac{2}{{\left( {x - y} \right)\left( {x + y} \right)}}.\dfrac{{\sqrt 3 }}{{\sqrt 2 }}.\left( {x + y} \right)\,\,\,\,\,\,\,\,\,\,\left( {x;y \ge 0 \Rightarrow x + y \ge 0} \right)\\
= \dfrac{{\sqrt 6 }}{{x - y}}
\end{array}\)
