Đáp án:
\(\begin{array}{l}
a)2\sqrt 5 - 1\\
b)\dfrac{{6\sqrt 5 }}{5} - \dfrac{{3\sqrt 3 }}{{14}}\\
c)1\\
d)\dfrac{{7\sqrt 6 }}{6}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)3\sqrt 5 - 10.\dfrac{1}{{\sqrt 5 }} + \sqrt 5 - 1\\
= 4\sqrt 5 - 2\sqrt 5 - 1\\
= 2\sqrt 5 - 1\\
b)2.\dfrac{{3\sqrt 5 }}{5} + 3.\dfrac{{3\sqrt 3 }}{7} - \dfrac{9}{{2\sqrt 3 }}\\
= \dfrac{{6\sqrt 5 }}{5} + \dfrac{{9\sqrt 3 }}{7} - \dfrac{{3\sqrt 3 }}{2}\\
= \dfrac{{6\sqrt 5 }}{5} - \dfrac{{3\sqrt 3 }}{{14}}\\
c)\left( {2 + \dfrac{{\sqrt 3 \left( {\sqrt 3 - 1} \right)}}{{ - \left( {\sqrt 3 - 1} \right)}}} \right).\left( {2 + \dfrac{{\sqrt 3 \left( {\sqrt 3 + 1} \right)}}{{\sqrt 3 + 1}}} \right)\\
= \left( {2 - \sqrt 3 } \right)\left( {2 + \sqrt 3 } \right)\\
= 4 - 3 = 1\\
d)\dfrac{{2\left( {\sqrt 6 + 2} \right) + 2\left( {\sqrt 6 - 2} \right)}}{{6 - 4}} - \dfrac{5}{{\sqrt 6 }}\\
= \dfrac{{4\sqrt 6 }}{2} - \dfrac{{5\sqrt 6 }}{6} = \dfrac{{7\sqrt 6 }}{6}
\end{array}\)
