Đáp án:
$\begin{array}{l}
a){\left( {\sqrt 2 + 1} \right)^3} - {\left( {\sqrt 2 - 1} \right)^3}\\
= \left( {\sqrt 2 + 1 - \sqrt 2 + 1} \right)\\
.\left[ {{{\left( {\sqrt 2 + 1} \right)}^2} + \left( {\sqrt 2 + 1} \right)\left( {\sqrt 2 - 1} \right) + {{\left( {\sqrt 2 - 1} \right)}^2}} \right]\\
= 2.\left( {2 + 2\sqrt 2 + 1 + 2 - 1 + 2 - 2\sqrt 2 + 1} \right)\\
= 2.7\\
= 14\\
b)\dfrac{1}{{\sqrt 5 + \sqrt 2 }} + \dfrac{1}{{\sqrt 5 - \sqrt 2 }}\\
= \dfrac{{\sqrt 5 - \sqrt 2 + \sqrt 5 + \sqrt 2 }}{{\left( {\sqrt 5 + \sqrt 2 } \right)\left( {\sqrt 5 - \sqrt 2 } \right)}}\\
= \dfrac{{2\sqrt 5 }}{{5 - 2}}\\
= \dfrac{{2\sqrt 5 }}{3}\\
c)\dfrac{{\sqrt {18} }}{{\sqrt 2 }} - \dfrac{{\sqrt {12} }}{{\sqrt 3 }}\\
= \sqrt 9 - \sqrt 4 \\
= 3 - 2\\
= 1\\
d)\sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} + \sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} \\
= \sqrt 5 + 1 + \sqrt 5 - 1\\
= 2\sqrt 5 \\
e)\sqrt {3 - 2\sqrt 2 } - \sqrt {3 + 2\sqrt 2 } \\
= \sqrt {{{\left( {\sqrt 2 - 1} \right)}^2}} - \sqrt {{{\left( {\sqrt 2 + 1} \right)}^2}} \\
= \sqrt 2 - 1 - \sqrt 2 - 1\\
= - 2\\
f)\dfrac{1}{{\sqrt 8 + \sqrt 7 }} + \sqrt {175} - 2\sqrt 2 \\
= \dfrac{{\sqrt 8 - \sqrt 7 }}{{8 - 7}} + \sqrt {25.7} - 2\sqrt 2 \\
= \sqrt 8 - \sqrt 7 + 5\sqrt 7 - 2\sqrt 2 \\
= 2\sqrt 2 + 4\sqrt 7 - 2\sqrt 2 \\
= 4\sqrt 7 \\
g)\left( {3\sqrt 2 - 2\sqrt 3 } \right)\left( {3\sqrt 2 + 2\sqrt 3 } \right)\\
= {\left( {3\sqrt 2 } \right)^2} - {\left( {2\sqrt 3 } \right)^2}\\
= 18 - 12\\
= 6
\end{array}$
