Đáp án:
\(\begin{array}{l}
a)6\\
d)4\\
b) - 4\sqrt 6 \\
e)2\sqrt 5 \\
c)1\\
f)2\sqrt 2 - 4
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\left| {3 - 2\sqrt 2 } \right| + \left| {3 + 2\sqrt 2 } \right|\\
= 3 - 2\sqrt 2 + 3 + 2\sqrt 2 \left( {do:3 > 2\sqrt 2 } \right)\\
= 6\\
d)\left| {3 + \sqrt 2 } \right| - \left| {1 - \sqrt 2 } \right|\\
= 3 + \sqrt 2 - \left( {\sqrt 2 - 1} \right)\left( {do:\sqrt 2 > 1} \right)\\
= 3 + \sqrt 2 - \sqrt 2 + 1 = 4\\
b)\left| {5 - 2\sqrt 6 } \right| - \left| {5 + 2\sqrt 6 } \right|\\
= 5 - 2\sqrt 6 - \left( {5 + 2\sqrt 6 } \right)\left( {do:5 > 2\sqrt 6 } \right)\\
= 5 - 2\sqrt 6 - 5 - 2\sqrt 6 \\
= - 4\sqrt 6 \\
e)\left| {\sqrt 5 - \sqrt 2 } \right| + \left| {\sqrt 5 + \sqrt 2 } \right|\\
= \sqrt 5 - \sqrt 2 + \sqrt 5 + \sqrt 2 \left( {do:\sqrt 5 > \sqrt 2 } \right)\\
= 2\sqrt 5 \\
c)\left| {2 - \sqrt 3 } \right| + \left| {1 - \sqrt 3 } \right|\\
= 2 - \sqrt 3 + \sqrt 3 - 1\left( {do:\left\{ \begin{array}{l}
2 > \sqrt 3 \\
1 < \sqrt 3
\end{array} \right.} \right)\\
= 1\\
f)\left| {\sqrt 2 + 1} \right| - \left| {\sqrt 2 - 5} \right|\\
= \sqrt 2 + 1 - \left( {5 - \sqrt 2 } \right)\left( {do:5 > \sqrt 2 } \right)\\
= \sqrt 2 + 1 - 5 + \sqrt 2 \\
= 2\sqrt 2 - 4
\end{array}\)
