Đáp án:
f) 7
Giải thích các bước giải:
\(\begin{array}{l}
a)\sqrt {4 + 2.2\sqrt 3 + 3} - \sqrt {9 - 2.3.\sqrt 3 + 3} \\
= \sqrt {{{\left( {2 + \sqrt 3 } \right)}^2}} - \sqrt {{{\left( {3 - \sqrt 3 } \right)}^2}} \\
= 2 + \sqrt 3 - 3 + \sqrt 3 \\
= - 1 + 2\sqrt 3 \\
c)\dfrac{{\sqrt {7 - 2\sqrt 6 } - 1}}{{1 - 7 + 2\sqrt 6 }} - \dfrac{{\sqrt {7 + 2\sqrt 6 } + 1}}{{7 + 2\sqrt 6 - 1}}\\
= \dfrac{{\sqrt {{{\left( {\sqrt 6 - 1} \right)}^2}} - 1}}{{2\sqrt 6 - 6}} - \dfrac{{\sqrt {{{\left( {\sqrt 6 + 1} \right)}^2}} + 1}}{{2\sqrt 6 + 6}}\\
= \dfrac{{\sqrt 6 - 2}}{{2\sqrt 6 - 6}} - \dfrac{{\sqrt 6 + 2}}{{2\sqrt 6 + 6}}\\
= \dfrac{{\sqrt 6 - 2}}{{\sqrt 6 \left( {2 - \sqrt 6 } \right)}} - \dfrac{{\sqrt 6 + 2}}{{\sqrt 6 \left( {2 + \sqrt 6 } \right)}}\\
= - \dfrac{1}{{\sqrt 6 }} - \dfrac{1}{{\sqrt 6 }} = - \dfrac{{\sqrt 6 }}{3}\\
e)\left[ {\dfrac{{\sqrt 3 + \sqrt 2 }}{{3 - 2}} - \dfrac{{\sqrt 3 \left( {1 - \sqrt 2 } \right)}}{{1 - \sqrt 2 }} - \sqrt 3 } \right]\left( {\sqrt 2 - \sqrt 3 } \right)\\
= \left( {\sqrt 3 + \sqrt 2 - \sqrt 3 - \sqrt 3 } \right)\left( {\sqrt 2 - \sqrt 3 } \right)\\
= {\left( {\sqrt 2 - \sqrt 3 } \right)^2} = 5 - 2\sqrt 6 \\
b)25.2 - 10.2.\sqrt 3 + 6 + 20\sqrt 3 \\
= 56\\
f)\dfrac{{2\left( {\sqrt 3 - 1} \right)}}{{3 - 1}} - \dfrac{{\sqrt 3 + 2}}{{3 - 4}} + \dfrac{{12\left( {\sqrt 3 - 3} \right)}}{{3 - 9}}\\
= \sqrt 3 - 1 + \sqrt 3 + 2 - \dfrac{{12\left( {\sqrt 3 - 3} \right)}}{6}\\
= 2\sqrt 3 + 1 - 2\left( {\sqrt 3 - 3} \right)\\
= 7
\end{array}\)
