Đáp án + Giải thích các bước giải:
$\begin{array}{l} Bài 5:)\\ a)\sqrt {12} + \sqrt {48} - \sqrt {75} + \sqrt {108} - \sqrt {147} \\ = 2\sqrt 3 + 4\sqrt 3 - 5\sqrt 3 - 7\sqrt 3 = - 6\sqrt 7 \\ b)6\sqrt {18} - 5\sqrt 8 + 4\sqrt {32} + 3\sqrt {128} \\ = 6.3\sqrt 2 - 5.2\sqrt 2 + 4.4\sqrt 2 + 3.8\sqrt 2 \\ = 18\sqrt 2 - 10\sqrt 2 + 16\sqrt 2 + 24\sqrt 2 = 48\sqrt 2 \\ c)\left( {\sqrt {28} - 2\sqrt {14} + \sqrt 7 } \right).\sqrt 7 + 7\sqrt 8 \\ = \left( {2\sqrt 7 - 2\sqrt {14} + \sqrt 7 } \right).\sqrt 7 + 7.2\sqrt 2 \\ = 3.7 - 2.\sqrt {14} .\sqrt 7 + 14\sqrt 2 = 21 - 14\sqrt 2 + 14\sqrt 2 \\ = 21\\ d)\left( {15\sqrt {50} + 5\sqrt {200} - 3\sqrt {450} } \right):\sqrt {10} \\ = \left( {15.5\sqrt 2 + 5.10\sqrt 2 - 3.15\sqrt 2 } \right):\sqrt {10} \\ = 80\sqrt 2 :\sqrt {10} = 16\sqrt 5 \\ Bài 6\\ a)\sqrt {{{\left( {\sqrt 3 - 2} \right)}^2}} + \sqrt {{{\left( {3 - \sqrt 3 } \right)}^2}} \\=|\sqrt{3}-2|+|3-\sqrt{3}|\\ = 2 - \sqrt 3 + 3 - \sqrt 3 = 5 - 2\sqrt 3 \\ b)\sqrt {6 + 2\sqrt 5 } + \sqrt {6 - 2\sqrt 5 } \\ =\sqrt{5+2.\sqrt{5}.1+1}+\sqrt{5-2.\sqrt{5}.1+1}\\= \sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} + \sqrt {{{\left( {\sqrt 5 - 1} \right)}^2}} \\ = \sqrt 5 + 1 + \sqrt 5 - 1 = 2\sqrt 5 \\ c)\sqrt {11 + 6\sqrt 2 } - \sqrt {11 - 6\sqrt 2 } \\ = \sqrt {9 + 2.3.\sqrt 2 + 2} - \sqrt {9 - 2.3.\sqrt 2 + 2} \\ = \sqrt {{{\left( {3 + \sqrt 2 } \right)}^2}} - \sqrt {{{\left( {3 - \sqrt 2 } \right)}^2}} \\ = 3 + \sqrt 2 - 3 + \sqrt 2 = 2\sqrt 2 \end{array}$
