Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
3\sqrt 2 - 4\sqrt {18} + 2.\sqrt {32} - \sqrt {50} \\
= 3\sqrt 2 - 4\sqrt {{3^2}.2} + 2.\sqrt {{2^5}} - \sqrt {{5^2}.2} \\
= 3\sqrt 2 - 4.3.\sqrt 2 + {2.2^2}.\sqrt 2 - 5.\sqrt 2 \\
= 3\sqrt 2 - 12\sqrt 2 + 8\sqrt 2 - 5\sqrt 2 \\
= - 6\sqrt 2 \\
2,\\
\sqrt {50} - \sqrt {18} + \sqrt {200} - \sqrt {162} \\
= \sqrt {{5^2}.2} - \sqrt {{3^2}.2} + \sqrt {{{10}^2}.2} - \sqrt {{9^2}.2} \\
= 5\sqrt 2 - 3\sqrt 2 + 10\sqrt 2 - 9\sqrt 2 \\
= 3\sqrt 2 \\
3,\\
\dfrac{1}{2}\sqrt {48} - 2\sqrt {75} - \dfrac{{\sqrt {33} }}{{\sqrt {11} }} + 5\sqrt {1\dfrac{1}{3}} \\
= \dfrac{1}{2}\sqrt {{4^2}.3} - 2.\sqrt {{5^2}.3} - \dfrac{{\sqrt 3 .\sqrt {11} }}{{\sqrt {11} }} + 5\sqrt {\dfrac{4}{3}} \\
= \dfrac{1}{2}.4.\sqrt 3 - 2.5.\sqrt 3 - \sqrt 3 + 5.\dfrac{2}{{\sqrt 3 }}\\
= 2\sqrt 3 - 10\sqrt 3 - \sqrt 3 + \dfrac{{10}}{{\sqrt 3 }}\\
= - 9\sqrt 3 + \dfrac{{10}}{{\sqrt 3 }} = \dfrac{{ - 9.{{\sqrt 3 }^2} + 10}}{{\sqrt 3 }} = \dfrac{{ - 17}}{{\sqrt 3 }}\\
4,\\
3\sqrt {12} - 4\sqrt {27} + 5\sqrt {48} \\
= 3.\sqrt {{2^2}.3} - 4.\sqrt {{3^2}.3} + 5.\sqrt {{4^2}.3} \\
= 3.2.\sqrt 3 - 4.3.\sqrt 3 + 5.4.\sqrt 3 \\
= 6\sqrt 3 - 12\sqrt 3 + 20\sqrt 3 \\
= 14\sqrt 3 \\
5,\\
\sqrt {125} - 2\sqrt {20} - 3\sqrt {80} + 4\sqrt {45} \\
= \sqrt {{5^2}.5} - 2.\sqrt {{2^2}.5} - 3.\sqrt {{4^2}.5} + 4.\sqrt {{3^2}.5} \\
= 5\sqrt 5 - 2.2\sqrt 5 - 3.4\sqrt 5 + 4.3\sqrt 5 \\
= 5\sqrt 5 - 4\sqrt 5 - 12\sqrt 5 + 12\sqrt 5 \\
= \sqrt 5 \\
15,\\
\dfrac{6}{{3\sqrt 2 + 2\sqrt 3 }} = \dfrac{{6.\left( {3\sqrt 2 - 2\sqrt 3 } \right)}}{{\left( {3\sqrt 2 + 2\sqrt 3 } \right)\left( {3\sqrt 2 - 2\sqrt 3 } \right)}}\\
= \dfrac{{18\sqrt 2 - 12\sqrt 3 }}{{{{\left( {3\sqrt 2 } \right)}^2} - {{\left( {2\sqrt 3 } \right)}^2}}} = \dfrac{{18\sqrt 2 - 12\sqrt 3 }}{6} = 3\sqrt 2 - 2\sqrt 3 \\
16,\\
\left( {\sqrt {75} - 3\sqrt 2 - \sqrt {12} } \right)\left( {\sqrt 3 + \sqrt 2 } \right)\\
= \left( {\sqrt {{5^2}.3} - 3\sqrt 2 - \sqrt {{2^2}.3} } \right)\left( {\sqrt 3 + \sqrt 2 } \right)\\
= \left( {5\sqrt 3 - 3\sqrt 2 - 2\sqrt 3 } \right)\left( {\sqrt 3 + \sqrt 2 } \right)\\
= 3.\left( {\sqrt 3 - \sqrt 2 } \right)\left( {\sqrt 3 + \sqrt 2 } \right)\\
= 3.\left( {{{\sqrt 3 }^2} - {{\sqrt 2 }^2}} \right)\\
= 3.\left( {3 - 2} \right) = 3\\
17,\\
\dfrac{{\sqrt 5 + \sqrt 3 }}{{\sqrt 5 - \sqrt 3 }} + \dfrac{{\sqrt 5 - \sqrt 3 }}{{\sqrt 5 + \sqrt 3 }}\\
= \dfrac{{{{\left( {\sqrt 5 + \sqrt 3 } \right)}^2} + {{\left( {\sqrt 5 - \sqrt 3 } \right)}^2}}}{{\left( {\sqrt 5 - \sqrt 3 } \right)\left( {\sqrt 5 + \sqrt 3 } \right)}}\\
= \dfrac{{5 + 2\sqrt {15} + 3 + 5 - 2\sqrt {15} + 3}}{{5 - 3}}\\
= \dfrac{{16}}{2} = 8
\end{array}\)
