Đáp án:
h. \(\sqrt {9 - 3\sqrt 3 } \)
Giải thích các bước giải:
\(\begin{array}{l}
e.\dfrac{{\sqrt 5 + 2 + \sqrt 5 - 2}}{{5 - 4}} = 2\sqrt 5 \\
f.\dfrac{{4\sqrt 3 - 4}}{{3 - 1}} + \dfrac{{\sqrt 3 + 2}}{{3 - 2}} + \dfrac{{6\sqrt 3 - 18}}{{3 - 9}}\\
= \dfrac{{4\sqrt 3 - 4}}{2} + \dfrac{{\sqrt 3 + 2}}{1} - \dfrac{{6\sqrt 3 - 18}}{6}\\
= \dfrac{{24\sqrt 3 - 24 + 12\sqrt 3 + 24 - 12\sqrt 3 + 36}}{{12}}\\
= \dfrac{{24\sqrt 3 + 36}}{{12}}\\
= 2\sqrt 3 + 3\\
g.2.3\sqrt 3 - 6.\dfrac{2}{{\sqrt 3 }} + \dfrac{3}{5}.5\sqrt 3 \\
= 9\sqrt 3 - 4\sqrt 3 = 5\sqrt 3 \\
h.\left( {2\sqrt 6 - 4\sqrt 3 + 5\sqrt 2 - \dfrac{1}{4}.2\sqrt 2 } \right).3\sqrt 6 \\
= \left( {2\sqrt 6 - 4\sqrt 3 + \dfrac{{9\sqrt 2 }}{2}} \right).3\sqrt 6 \\
= 6.6 - 36\sqrt 2 + 27\sqrt 3 \\
= 36 - 36\sqrt 2 + 27\sqrt 3 \\
m.\sqrt {\dfrac{{2 - \sqrt 3 }}{{2 + \sqrt 3 }} + \sqrt {\dfrac{{{{\left( {2 + \sqrt 3 } \right)}^2}}}{{4 - 3}}} } \\
= \sqrt {\dfrac{{2 - \sqrt 3 }}{{2 + \sqrt 3 }} + 2 + \sqrt 3 } \\
= \sqrt {\dfrac{{2 - \sqrt 3 + 4 + 4\sqrt 3 + 3}}{{2 + \sqrt 3 }}} \\
= \sqrt {\dfrac{{9 + 3\sqrt 3 }}{{2 + \sqrt 3 }}} \\
= \sqrt {\dfrac{{\left( {9 + 3\sqrt 3 } \right)\left( {2 - \sqrt 3 } \right)}}{{4 - 3}}} \\
= \sqrt {18 + 6\sqrt 3 - 9\sqrt 3 - 9} \\
= \sqrt {9 - 3\sqrt 3 }
\end{array}\)
