Đáp án:
\(a. - 5\sqrt 3 \)
Giải thích các bước giải:
\(\begin{array}{l}
a.2.3\sqrt 3 - 4\sqrt 3 + 2.4\sqrt 3 - 3.5\sqrt 3 \\
= \left( {6 - 4 + 8 - 15} \right)\sqrt 3 \\
= - 5\sqrt 3 \\
b.10.6\sqrt 2 - \dfrac{5}{3}.9\sqrt 2 + 8\sqrt 2 - 2.5\sqrt 2 + 7\sqrt 2 \\
= \left( {60 - 15 + 8 - 10 + 7} \right)\sqrt 2 \\
= 50\sqrt 2 \\
c.3.5\sqrt 5 - 2\sqrt 2 + \dfrac{1}{2}.5\sqrt 2 - \dfrac{1}{3}.3\sqrt 5 \\
= \left( { - 2 + \dfrac{5}{2}} \right)\sqrt 2 + \left( {15 - 1} \right)\sqrt 5 \\
= \dfrac{{\sqrt 2 }}{2} + 14\sqrt 5 \\
d.\dfrac{{1 - \sqrt 5 + 1 + \sqrt 5 }}{{\left( {1 - \sqrt 5 } \right)\left( {1 + \sqrt 5 } \right)}}\\
= \dfrac{2}{{1 - 5}} = \dfrac{2}{{ - 4}} = - \dfrac{1}{2}\\
e.\dfrac{1}{{\sqrt 2 - \sqrt 3 }} - \dfrac{1}{{\sqrt 2 + \sqrt 3 }}\\
= \dfrac{{\sqrt 2 + \sqrt 3 - \sqrt 2 + \sqrt 3 }}{{\left( {\sqrt 2 - \sqrt 3 } \right)\left( {\sqrt 2 + \sqrt 3 } \right)}}\\
= \dfrac{{2\sqrt 3 }}{{2 - 3}} = - 2\sqrt 3
\end{array}\)
