Đáp án:
\(\begin{array}{l}
a) - 5\sqrt 5 \\
c)\dfrac{{7\sqrt 3 }}{6}\\
e)4\\
b)22\\
d) - \dfrac{5}{{6\sqrt 2 }}\\
f)2\sqrt 3
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)5\sqrt 5 - 4.3\sqrt 5 + 3.2\sqrt 5 - 4\sqrt 5 \\
= \left( {5 - 12 + 6 - 4} \right)\sqrt 5 \\
= - 5\sqrt 5 \\
c)2.\dfrac{{3\sqrt 3 }}{2} - \dfrac{{4\sqrt 3 }}{3} - \dfrac{2}{5}.\dfrac{{5\sqrt 3 }}{4}\\
= 3\sqrt 3 - \dfrac{{4\sqrt 3 }}{3} - \dfrac{{\sqrt 3 }}{2}\\
= \left( {3 - \dfrac{4}{3} - \dfrac{1}{2}} \right)\sqrt 3 \\
= \dfrac{{7\sqrt 3 }}{6}\\
e)\left[ {1 + \dfrac{{\sqrt 5 \left( {\sqrt 5 - 1} \right)}}{{ - \left( {\sqrt 5 - 1} \right)}}} \right].\left[ {\dfrac{{\sqrt 5 \left( {\sqrt 5 + 1} \right)}}{{\sqrt 5 + 1}} + 1} \right]\\
= \left( {1 - \sqrt 5 } \right)\left( {\sqrt 5 + 1} \right)\\
= 5 - 1 = 4\\
b)\left( {3\sqrt {11} - 3\sqrt 2 - \sqrt {11} } \right).\sqrt {11} + 3\sqrt {22} \\
= 2\sqrt {11} .\sqrt {11} - 3\sqrt {22} + 3\sqrt {22} \\
= 2.11 = 22\\
d)3.\dfrac{3}{{2\sqrt 2 }} - \dfrac{7}{{\sqrt 2 }} + \dfrac{5}{{3\sqrt 2 }}\\
= \left( {\dfrac{9}{2} - 7 + \dfrac{5}{3}} \right).\dfrac{1}{{\sqrt 2 }}\\
= - \dfrac{5}{{6\sqrt 2 }}\\
f)\dfrac{{\sqrt 3 + \sqrt 2 + \sqrt 3 - \sqrt 2 }}{{3 - 2}}\\
= 2\sqrt 3
\end{array}\)
