Đáp án:
\(\begin{array}{l}
23)\sqrt 2 \\
25) - 30 - 16\sqrt 2 \\
24)\dfrac{{2\sqrt 3 + 9}}{3}\\
26) - 4 + \sqrt 2
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
23)\dfrac{{\sqrt 3 \left( {\sqrt 3 + 2} \right)}}{{\sqrt 3 }} + \dfrac{{\sqrt 2 \left( {\sqrt 2 + 1} \right)}}{{\sqrt 2 + 1}} - \dfrac{{2 + \sqrt 3 }}{{4 - 3}}\\
= \sqrt 3 + 2 + \sqrt 2 - 2 - \sqrt 3 \\
= \sqrt 2 \\
25)\dfrac{{\left( {8 + 2\sqrt 2 } \right)\left( {3 + \sqrt 2 } \right)}}{{\left( {3 + \sqrt 2 } \right)\left( {3 - \sqrt 2 } \right)}} - \dfrac{{\sqrt 2 \left( {\sqrt 2 + 3} \right)}}{{\sqrt 2 }} + \dfrac{{\sqrt 2 \left( {1 + \sqrt 2 } \right)}}{{1 - 2}}\\
= \dfrac{{24 + 8\sqrt 2 + 6\sqrt 2 + 4}}{{3 - 4}} - \sqrt 2 - 3 - \sqrt 2 - 2\\
= - 28 - 14\sqrt 2 + 3 - 2\sqrt 2 - 5\\
= - 30 - 16\sqrt 2 \\
24)\dfrac{{\sqrt 5 \left( {\sqrt 5 + 2} \right)}}{{\sqrt 5 }} + \dfrac{{5\sqrt 3 + 3}}{3} - \sqrt 5 - \sqrt 3 \\
= \sqrt 5 + 2 + \dfrac{{5\sqrt 3 + 3}}{3} - \sqrt 5 - \sqrt 3 \\
= 2 - \sqrt 3 + \dfrac{{5\sqrt 3 + 3}}{3}\\
= \dfrac{{6 - 3\sqrt 3 + 5\sqrt 3 + 3}}{3}\\
= \dfrac{{2\sqrt 3 + 9}}{3}\\
26)\sqrt {7 - 2.2.\sqrt 7 + 4} + \dfrac{{3\left( {2 + \sqrt 7 } \right)}}{{4 - 7}} + \dfrac{{\sqrt 2 \left( {\sqrt 2 + 1} \right)}}{{\sqrt 2 + 1}}\\
= \sqrt {{{\left( {\sqrt 7 - 2} \right)}^2}} - 2 - \sqrt 7 + \sqrt 2 \\
= \sqrt 7 - 2 - 2 - \sqrt 7 + \sqrt 2 \\
= - 4 + \sqrt 2
\end{array}\)
