Đáp án:
\(\begin{array}{l}
a)2\sqrt 3 \\
b) - \sqrt 2 \\
c)\dfrac{1}{2}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)7.3\sqrt 2 + 2\sqrt 3 - 3.7\sqrt 2 \\
= 2\sqrt 3 \\
b)\sqrt {{{\left( {\sqrt 5 - 2\sqrt 2 } \right)}^2}} - \sqrt {18 - 2.3\sqrt 2 .\sqrt 5 + 5} \\
= \sqrt {{{\left( {\sqrt 5 - 2\sqrt 2 } \right)}^2}} - \sqrt {{{\left( {3\sqrt 2 - \sqrt 5 } \right)}^2}} \\
= \left| {\sqrt 5 - 2\sqrt 2 } \right| - \left| {3\sqrt 2 - \sqrt 5 } \right|\\
= 2\sqrt 2 - \sqrt 5 - 3\sqrt 2 + \sqrt 5 \\
= - \sqrt 2 \\
c)\dfrac{{3\left( {\sqrt 7 + 1} \right)}}{{7 - 1}} - \dfrac{{\sqrt 7 \left( {1 - \sqrt 3 } \right)}}{{2\left( {1 - \sqrt 3 } \right)}}\\
= \dfrac{{\sqrt 7 + 1}}{2} - \dfrac{{\sqrt 7 }}{2}\\
= \dfrac{1}{2}
\end{array}\)
