Đáp án:
\(\begin{array}{l}
a)8\sqrt 2 \\
d)\sqrt 6 \\
b)\sqrt 6 - \sqrt 5 - 1\\
c)5\\
e)\dfrac{{9\sqrt 2 }}{2}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)3\sqrt 2 + 4.2\sqrt 2 - 3\sqrt 2 \\
= \left( {3 + 8 - 3} \right)\sqrt 2 \\
= 8\sqrt 2 \\
d)D = \sqrt {2 + \sqrt 3 } + \sqrt {2 - \sqrt 3 } \\
\to {D^2} = 2 + \sqrt 3 + 2\sqrt {\left( {2 + \sqrt 3 } \right)\left( {2 - \sqrt 3 } \right)} + 2 - \sqrt 3 \\
= 4 + 2\sqrt {4 - 3} \\
= 4 + 2 = 6\\
\to D = \sqrt 6 \\
b)\dfrac{{2\left( {\sqrt 6 + 2} \right)}}{{6 - 4}} - \dfrac{{4\left( {3 + \sqrt 5 } \right)}}{{9 - 5}}\\
= \sqrt 6 + 2 - \left( {3 + \sqrt 5 } \right)\\
= \sqrt 6 - \sqrt 5 - 1\\
c)4\sqrt 6 - 2\sqrt 6 + \dfrac{{3\left( {3 - \sqrt 6 } \right)}}{{9 - 6}} - \sqrt {6 - 2.2.\sqrt 6 + 4} \\
= 2\sqrt 6 + 3 - \sqrt 6 - \sqrt {{{\left( {\sqrt 6 - 2} \right)}^2}} \\
= \sqrt 6 + 3 - \left( {\sqrt 6 - 2} \right)\\
= 5\\
e)\dfrac{{\sqrt 2 }}{2} + \dfrac{{3\sqrt 2 }}{2} + \dfrac{{5\sqrt 2 }}{2}\\
= \left( {\dfrac{1}{2} + \dfrac{3}{2} + \dfrac{5}{2}} \right)\sqrt 2 \\
= \dfrac{{9\sqrt 2 }}{2}
\end{array}\)
