Đáp án:
\(\begin{array}{l}
1,\,\,\,\, - 6\sqrt 2 \\
2,\,\,\,\,3\sqrt 2 \\
3,\,\,\,\, - 2\sqrt 5 \\
4,\,\,\,\,4\sqrt 3 \\
5,\,\,\,\, - \dfrac{{17\sqrt 3 }}{3}\\
6,\,\,\,\,14\sqrt 3 \\
7,\,\,\,\,3\sqrt 3 \\
8,\,\,\,\,\sqrt 2 \\
9,\,\,\,\,4\sqrt 5 \\
10,\,\,\,\, - 4\sqrt 6 \\
11,\,\,\,\,8\sqrt 2 \\
12,\,\,\,\,9\sqrt 2 \\
13,\,\,\,\,\sqrt 5 \\
14,\,\,\,\, - \sqrt 7 \\
15,\,\,\,\,\dfrac{7}{2}\sqrt 2 \\
16,\,\,\,\,10\sqrt 2 + \sqrt 3 \\
17,\,\,\,\,7\sqrt 3 \\
18,\,\,\,\,4\sqrt 3
\end{array}\)
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 {9.2} + 2\sqrt {16.2} - \sqrt {25.2} \\
= 3\sqrt 2 - 4.\sqrt {{3^2}.2} + 2.\sqrt {{4^2}.2} - \sqrt {{5^2}.2} \\
= 3\sqrt 2 - 4.3\sqrt 2 + 2.4\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 {25.2} - \sqrt {9.2} + \sqrt {100.2} - \sqrt {81.2} \\
= \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,\\
5\sqrt 5 + \sqrt {20} - 3\sqrt {45} \\
= 5\sqrt 5 + \sqrt {4.5} - 3\sqrt {9.5} \\
= 5\sqrt 5 + \sqrt {{2^2}.5} - 3\sqrt {{3^2}.5} \\
= 5\sqrt 5 + 2\sqrt 5 - 3.3\sqrt 5 \\
= 5\sqrt 5 + 2\sqrt 5 - 9\sqrt 5 \\
= - 2\sqrt 5 \\
4,\\
5\sqrt {48} - 4\sqrt {27} - 2\sqrt {75} + \sqrt {108} \\
= 5\sqrt {16.3} - 4\sqrt {9.3} - 2\sqrt {25.3} + \sqrt {36.3} \\
= 5\sqrt {{4^2}.3} - 4\sqrt {{3^2}.3} - 2\sqrt {{5^2}.3} + \sqrt {{6^2}.3} \\
= 5.4\sqrt 3 - 4.3\sqrt 3 - 2.5\sqrt 3 + 6\sqrt 3 \\
= 20\sqrt 3 - 12\sqrt 3 - 10\sqrt 3 + 6\sqrt 3 \\
= 4\sqrt 3 \\
5,\\
\dfrac{1}{2}\sqrt {48} - 2\sqrt {75} - \dfrac{{\sqrt {33} }}{{\sqrt {11} }} + 5\sqrt {1\dfrac{1}{3}} \\
= \dfrac{1}{2}\sqrt {16.3} - 2\sqrt {25.3} - \sqrt {\dfrac{{33}}{{11}}} + 5\sqrt {\dfrac{4}{3}} \\
= \dfrac{1}{2}.\sqrt {{4^2}.3} - 2.\sqrt {{5^2}.3} - \sqrt 3 + 5\sqrt {\dfrac{4}{9}.3} \\
= \dfrac{1}{2}.4\sqrt 3 - 2.5\sqrt 3 - \sqrt 3 + 5.\sqrt {{{\left( {\dfrac{2}{3}} \right)}^2}.3} \\
= 2\sqrt 3 - 10\sqrt 3 - \sqrt 3 + 5.\dfrac{2}{3}\sqrt 3 \\
= 2\sqrt 3 - 10\sqrt 3 - \sqrt 3 + \dfrac{{10}}{3}\sqrt 3 \\
= - \dfrac{{17\sqrt 3 }}{3}\\
6,\\
3\sqrt {12} - 4\sqrt {27} + 5\sqrt {48} \\
= 3.\sqrt {4.3} - 4\sqrt {9.3} + 5\sqrt {16.3} \\
= 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 \\
7,\\
\sqrt {12} + 5\sqrt 3 - \sqrt {48} \\
= \sqrt {4.3} + 5\sqrt 3 - \sqrt {16.3} \\
= \sqrt {{2^2}.3} + 5\sqrt 3 - \sqrt {{4^2}.3} \\
= 2\sqrt 3 + 5\sqrt 3 - 4\sqrt 3 \\
= 3\sqrt 3 \\
8,\\
2\sqrt {32} + 4\sqrt 8 - 5\sqrt {18} \\
= 2\sqrt {16.2} + 4\sqrt {4.2} - 5\sqrt {9.2} \\
= 2\sqrt {{4^2}.2} + 4\sqrt {{2^2}.2} - 5\sqrt {{3^2}.2} \\
= 2.4\sqrt 2 + 4.2\sqrt 2 - 5.3\sqrt 2 \\
= 8\sqrt 2 + 8\sqrt 2 - 15\sqrt 2 \\
= \sqrt 2 \\
9,\\
3\sqrt {20} - 2\sqrt {45} + 4\sqrt 5 \\
= 3.\sqrt {4.5} - 2.\sqrt {9.5} + 4\sqrt 5 \\
= 3.\sqrt {{2^2}.5} - 2.\sqrt {{3^2}.5} + 4\sqrt 5 \\
= 3.2\sqrt 5 - 2.3\sqrt 5 + 4\sqrt 5 \\
= 6\sqrt 5 - 6\sqrt 5 + 4\sqrt 5 \\
= 4\sqrt 5 \\
10,\\
2\sqrt {24} - 2\sqrt {54} + 3\sqrt 6 - \sqrt {150} \\
= 2\sqrt {4.6} - 2.\sqrt {9.6} + 3\sqrt 6 - \sqrt {25.6} \\
= 2\sqrt {{2^2}.6} - 2\sqrt {{3^2}.6} + 3\sqrt 6 - \sqrt {{5^2}.6} \\
= 2.2\sqrt 6 - 2.3\sqrt 6 + 3\sqrt 6 - 5\sqrt 6 \\
= 4\sqrt 6 - 6\sqrt 6 + 3\sqrt 6 - 5\sqrt 6 \\
= - 4\sqrt 6 \\
11,\\
2\sqrt {18} - 7\sqrt 2 + \sqrt {162} \\
= 2\sqrt {9.2} - 7\sqrt 2 + \sqrt {81.2} \\
= 2\sqrt {{3^2}.2} - 7\sqrt 2 + \sqrt {{9^2}.2} \\
= 2.3\sqrt 2 - 7\sqrt 2 + 9\sqrt 2 \\
= 6\sqrt 2 - 7\sqrt 2 + 9\sqrt 2 \\
= 8\sqrt 2 \\
12,\\
3\sqrt 8 - 4\sqrt {18} + 5\sqrt {32} - \sqrt {50} \\
= 3\sqrt {4.2} - 4\sqrt {9.2} + 5\sqrt {16.2} - \sqrt {25.2} \\
= 3.\sqrt {{2^2}.2} - 4\sqrt {{3^2}.2} + 5\sqrt {{4^2}.2} - \sqrt {{5^2}.2} \\
= 3.2\sqrt 2 - 4.3\sqrt 2 + 5.4\sqrt 2 - 5\sqrt 2 \\
= 6\sqrt 2 - 12\sqrt 2 + 20\sqrt 2 - 5\sqrt 2 \\
= 9\sqrt 2 \\
13,\\
\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 \\
14,\\
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 \\
15,\\
3\sqrt 2 + \sqrt 8 + \dfrac{1}{2}\sqrt {50} - \sqrt {32} \\
= 3\sqrt 2 + \sqrt {4.2} + \dfrac{1}{2}\sqrt {25.2} - \sqrt {16.2} \\
= 3\sqrt 2 + \sqrt {{2^2}.2} + \dfrac{1}{2}\sqrt {{5^2}.2} - \sqrt {{4^2}.2} \\
= 3\sqrt 2 + 2\sqrt 2 + \dfrac{1}{2}.5\sqrt 2 - 4\sqrt 2 \\
= 3\sqrt 2 + 2\sqrt 2 + \dfrac{5}{2}\sqrt 2 - 4\sqrt 2 \\
= \dfrac{7}{2}\sqrt 2 \\
16,\\
3\sqrt {50} - 2\sqrt {12} - \sqrt {18} + \sqrt {75} - \sqrt 8 \\
= 3\sqrt {25.2} - 2\sqrt {4.3} - \sqrt {9.2} + \sqrt {25.3} - \sqrt {4.2} \\
= 3.\sqrt {{5^2}.2} - 2\sqrt {{2^2}.3} - \sqrt {{3^2}.2} + \sqrt {{5^2}.3} - \sqrt {{2^2}.2} \\
= 3.5\sqrt 2 - 2.2\sqrt 3 - 3\sqrt 2 + 5\sqrt 3 - 2\sqrt 2 \\
= 15\sqrt 2 - 4\sqrt 3 - 3\sqrt 2 + 5\sqrt 3 - 2\sqrt 2 \\
= 10\sqrt 2 + \sqrt 3 \\
17,\\
2\sqrt {75} - 3\sqrt {12} + \sqrt {27} \\
= 2\sqrt {25.3} - 3\sqrt {4.3} + \sqrt {9.3} \\
= 2.\sqrt {{5^2}.3} - 3.\sqrt {{2^2}.3} + \sqrt {{3^2}.3} \\
= 2.5\sqrt 3 - 3.2\sqrt 3 + 3\sqrt 3 \\
= 10\sqrt 3 - 6\sqrt 3 + 3\sqrt 3 \\
= 7\sqrt 3 \\
18,\\
\sqrt {12} + \sqrt {75} - \sqrt {27} \\
= \sqrt {4.3} + \sqrt {25.3} - \sqrt {9.3} \\
= \sqrt {{2^2}.3} + \sqrt {{5^2}.3} - \sqrt {{3^2}.3} \\
= 2\sqrt 3 + 5\sqrt 3 - 3\sqrt 3 \\
= 4\sqrt 3
\end{array}\)
