Đáp án:
\(\begin{array}{l}
1,\,\,\,\, - 4\sqrt 3 \\
2,\,\,\,\,2\sqrt 2 \\
3,\,\,\,\,\dfrac{{ - 11\sqrt 2 }}{2}\\
4,\,\,\,\,10\\
5,\,\,\,\,\, - 8\\
6,\,\,\,\,\,35\\
7,\,\,\,\,\,\sqrt 3 - 3\\
8,\,\,\,\,\, - 6\sqrt 6 \\
14,\,\,\,\,\sqrt 5 \\
15,\,\,\,\, - \sqrt 7 \\
16,\,\,\,\,\, - \sqrt 7 - 19\sqrt {11}
\end{array}\)
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
3\sqrt 3 + 4\sqrt {12} - 5\sqrt {27} \\
= 3\sqrt 3 + 4.\sqrt {4.3} - 5\sqrt {9.3} \\
= 3\sqrt 3 + 4.\sqrt {{2^2}.3} - 5.\sqrt {{3^2}.3} \\
= 3\sqrt 3 + 4.2\sqrt 3 - 5.3\sqrt 3 \\
= 3\sqrt 3 + 8\sqrt 3 - 15\sqrt 3 \\
= - 4\sqrt 3 \\
2,\\
\sqrt {32} - \sqrt {50} + \sqrt {18} \\
= \sqrt {16.2} - \sqrt {25.2} + \sqrt {9.2} \\
= \sqrt {{4^2}.2} - \sqrt {{5^2}.2} + \sqrt {{3^2}.2} \\
= 4\sqrt 2 - 5\sqrt 2 + 3\sqrt 2 \\
= 2\sqrt 2 \\
3,\\
\sqrt {72} + \sqrt {4\dfrac{1}{2}} - \sqrt {32} - \sqrt {162} \\
= \sqrt {36.2} + \sqrt {\dfrac{9}{2}} - \sqrt {16.2} - \sqrt {81.2} \\
= \sqrt {{6^2}.2} + \sqrt {\dfrac{9}{4}.2} - \sqrt {{4^2}.2} - \sqrt {{9^2}.2} \\
= 6\sqrt 2 + \sqrt {{{\left( {\dfrac{3}{2}} \right)}^2}.2} - 4\sqrt 2 - 9\sqrt 2 \\
= 6\sqrt 2 + \dfrac{3}{2}\sqrt 2 - 4\sqrt 2 - 9\sqrt 2 \\
= \sqrt 2 .\left( {6 + \dfrac{3}{2} - 4 - 9} \right)\\
= \sqrt 2 .\left( { - \dfrac{{11}}{2}} \right)\\
= \dfrac{{ - 11\sqrt 2 }}{2}\\
4,\\
\left( {\sqrt {325} - \sqrt {117} + 2\sqrt {208} } \right):\sqrt {13} \\
= \left( {\sqrt {25.13} - \sqrt {9.13} + 2.\sqrt {16.13} } \right):\sqrt {13} \\
= \left( {\sqrt {{5^2}.13} - \sqrt {{3^2}.13} + 2\sqrt {{4^2}.13} } \right):\sqrt {13} \\
= \left( {5\sqrt {13} - 3\sqrt {13} + 2.4\sqrt {13} } \right):\sqrt {13} \\
= \left( {5\sqrt {13} - 3\sqrt {13} + 8\sqrt {13} } \right):\sqrt {13} \\
= 10\sqrt {13} :\sqrt {13} \\
= 10\\
5,\\
\left( {\sqrt {12} - \sqrt {48} - \sqrt {108} - \sqrt {192} } \right):2\sqrt 3 \\
= \left( {\sqrt {4.3} - \sqrt {16.3} - \sqrt {36.3} - \sqrt {64.3} } \right):2\sqrt 3 \\
= \left( {\sqrt {{2^2}.3} - \sqrt {{4^2}.3} - \sqrt {{6^2}.3} - \sqrt {{8^2}.3} } \right):2\sqrt 3 \\
= \left( {2\sqrt 3 - 4\sqrt 3 - 6\sqrt 3 - 8\sqrt 3 } \right):2\sqrt 3 \\
= \left( { - 16\sqrt 3 } \right):2\sqrt 3 \\
= - 8\\
6,\\
\left( {2\sqrt {112} - 5\sqrt 7 + 2\sqrt {63} - 2\sqrt {28} } \right).\sqrt 7 \\
= \left( {2\sqrt {16.7} - 5\sqrt 7 + 2\sqrt {9.7} - 2\sqrt {4.7} } \right).\sqrt 7 \\
= \left( {2.\sqrt {{4^2}.7} - 5\sqrt 7 + 2\sqrt {{3^2}.7} - 2.\sqrt {{2^2}.7} } \right).\sqrt 7 \\
= \left( {2.4\sqrt 7 - 5\sqrt 7 + 2.3\sqrt 7 - 2.2\sqrt 7 } \right).\sqrt 7 \\
= \left( {8\sqrt 7 - 5\sqrt 7 + 6\sqrt 7 - 4\sqrt 7 } \right).\sqrt 7 \\
= 5\sqrt 7 .\sqrt 7 \\
= 5.7\\
= 35\\
7,\\
\left( {2\sqrt {27} - 3\sqrt {48} + 3\sqrt {75} - \sqrt {192} } \right)\left( {1 - \sqrt 3 } \right)\\
= \left( {2\sqrt {9.3} - 3.\sqrt {16.3} + 3.\sqrt {25.3} - \sqrt {64.3} } \right)\left( {1 - \sqrt 3 } \right)\\
= \left( {2.\sqrt {{3^2}.3} - 3.\sqrt {{4^2}.3} + 3.\sqrt {{5^2}.3} - \sqrt {{8^2}.3} } \right)\left( {1 - \sqrt 3 } \right)\\
= \left( {2.3\sqrt 3 - 3.4\sqrt 3 + 3.5\sqrt 3 - 8\sqrt 3 } \right)\left( {1 - \sqrt 3 } \right)\\
= \left( {6\sqrt 3 - 12\sqrt 3 + 15\sqrt 3 - 8\sqrt 3 } \right)\left( {1 - \sqrt 3 } \right)\\
= \sqrt 3 .\left( {1 - \sqrt 3 } \right)\\
= \sqrt 3 - {\sqrt 3 ^2}\\
= \sqrt 3 - 3\\
8,\\
7\sqrt {24} - \sqrt {150} - 5\sqrt {54} \\
= 7\sqrt {4.6} - \sqrt {25.6} - 5.\sqrt {9.6} \\
= 7.\sqrt {{2^2}.6} - \sqrt {{5^2}.6} - 5.\sqrt {{3^2}.6} \\
= 7.2\sqrt 6 - 5\sqrt 6 - 5.3\sqrt 6 \\
= 14\sqrt 6 - 5\sqrt 6 - 15\sqrt 6 \\
= - 6\sqrt 6 \\
14,\\
\sqrt {125} - 2\sqrt {20} - 3\sqrt {80} + 4\sqrt {45} \\
= \sqrt {25.5} - 2\sqrt {4.5} - 3\sqrt {16.5} + 4\sqrt {9.5} \\
= \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,\\
2\sqrt {28} + 2\sqrt {63} - 3\sqrt {175} + \sqrt {112} \\
= 2\sqrt {4.7} + 2.\sqrt {9.7} - 3\sqrt {25.7} + \sqrt {16.7} \\
= 2\sqrt {{2^2}.7} + 2.\sqrt {{3^2}.7} - 3.\sqrt {{5^2}.7} + \sqrt {{4^2}.7} \\
= 2.2\sqrt 7 + 2.3\sqrt 7 - 3.5\sqrt 7 + 4\sqrt 7 \\
= 4\sqrt 7 + 6\sqrt 7 - 15\sqrt 7 + 4\sqrt 7 \\
= - \sqrt 7 \\
16,\\
10\sqrt {28} - 2\sqrt {275} - 3\sqrt {343} - \dfrac{3}{2}\sqrt {396} \\
= 10\sqrt {4.7} - 2.\sqrt {25.11} - 3\sqrt {49.7} - \dfrac{3}{2}\sqrt {36.11} \\
= 10\sqrt {{2^2}.7} - 2.\sqrt {{5^2}.11} - 3\sqrt {{7^2}.7} - \dfrac{3}{2}\sqrt {{6^2}.11} \\
= 10.2\sqrt 7 - 2.5\sqrt {11} - 3.7\sqrt 7 - \dfrac{3}{2}.6\sqrt {11} \\
= 20\sqrt 7 - 10\sqrt {11} - 21\sqrt 7 - 9\sqrt {11} \\
= \left( {20\sqrt 7 - 21\sqrt 7 } \right) + \left( { - 10\sqrt {11} - 9\sqrt {11} } \right)\\
= - \sqrt 7 - 19\sqrt {11}
\end{array}\)
