Đáp án:
\(\begin{array}{l}
a)21\\
b)41\\
c)6\sqrt 3 + 5\\
b)3\\
e) - 1 + 2\sqrt 3
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\left( {2\sqrt 7 - 2.\sqrt {14} + \sqrt 7 } \right).\sqrt 7 + 7.2.\sqrt 2 \\
= 3.7 - 2.7.\sqrt 2 + 7.2.\sqrt 2 \\
= 21\\
b)\left[ {\dfrac{{3 + 2\sqrt 2 }}{{9 - 8}} - \dfrac{{6\left( {2 - \sqrt 2 } \right)}}{{4 - 2}}} \right].\left( {3 + 5\sqrt 2 } \right)\\
= \left( {3 + 2\sqrt 2 - 3\left( {2 - \sqrt 2 } \right)} \right).\left( {3 + 5\sqrt 2 } \right)\\
= \left( {5\sqrt 2 - 3} \right).\left( {3 + 5\sqrt 2 } \right)\\
= {\left( {5\sqrt 2 } \right)^2} - 9\\
= 50 - 9 = 41\\
c)\dfrac{{4\left( {\sqrt 3 - 1} \right)}}{{3 - 1}} - \dfrac{{5\left( {2 + \sqrt 3 } \right)}}{{3 - 4}} + \dfrac{{6\left( {\sqrt 3 + 3} \right)}}{{3 - 9}}\\
= 2\left( {\sqrt 3 - 1} \right) + 5\left( {2 + \sqrt 3 } \right) - \left( {\sqrt 3 + 3} \right)\\
= 2\sqrt 3 - 2 + 10 + 5\sqrt 3 - \sqrt 3 - 3\\
= 6\sqrt 3 + 5\\
b)\left| {\sqrt 3 - 2} \right| + \left| {1 + \sqrt 3 } \right|\\
= 2 - \sqrt 3 + 1 + \sqrt 3 \\
= 3\\
e)\sqrt {4 + 2.2.\sqrt 3 + 3} - \sqrt {9 - 2.3.\sqrt 3 + 3} \\
= \sqrt {{{\left( {2 + \sqrt 3 } \right)}^2}} - \sqrt {{{\left( {3 - \sqrt 3 } \right)}^2}} \\
= 2 + \sqrt 3 - \left( {3 - \sqrt 3 } \right)\\
= - 1 + 2\sqrt 3
\end{array}\)
