Răspuns:
[tex]a)3 \sqrt{10} - 2(4 \sqrt{10} + 3) + 5 \sqrt{10} = \\ = 3 \sqrt{10} - 8 \sqrt{10} - 6 + 5 \sqrt{10} = \\ = - 5 \sqrt{10} - 6 + 5 \sqrt{10} = - 6[/tex]
[tex]b) - 7(3 \sqrt{2} + \sqrt{3} ) + 3( \sqrt{8} + \sqrt{12} ) = \\ = - 21 \sqrt{2} - 7 \sqrt{3} + 3 \sqrt{8} + 3 \sqrt{12} = \\ = - 21 \sqrt{2} - 7 \sqrt{3} + 3 \times 2 \sqrt{2} + 3 \times 2 \sqrt{3} \\ = - 21 \sqrt{2} - 7 \sqrt{3} + 6 \sqrt{2} + 6 \sqrt{3} = - 15 \sqrt{2} - \sqrt{3} [/tex]
[tex]c)2( \sqrt{20} - \sqrt{6} ) - 5( \sqrt{5} + 3 \sqrt{6} ) = \\ = 2 \sqrt{20} - 2 \sqrt{6} - 5 \sqrt{5} - 15 \sqrt{6} \\ = 2 \times 2 \sqrt{5} - 2 \sqrt{6} - 5 \sqrt{5} - 15 \sqrt{6} \\ = 4 \sqrt{5} - 2 \sqrt{6} - 5 \sqrt{5} - 15 \sqrt{6} = - \sqrt{5} - 17 \sqrt{6} [/tex]
[tex]d) \sqrt{3} ( \sqrt{5} + \sqrt{2} ) + 2(3 \sqrt{15} - \sqrt{96} ) = \\ = \sqrt{15} + \sqrt{6} + 6 \sqrt{15} - 2 \sqrt{96} \\ = 7 \sqrt{15} + \sqrt{6} - 2 \times 4 \sqrt{6} \\ = 7 \sqrt{15} + \sqrt{6} - 8 \sqrt{6} = 7 \sqrt{15} - 7 \sqrt{6} [/tex]
[tex]e)2 \sqrt{3} (3 \sqrt{5} - 4 \sqrt{7} ) + \sqrt{84} - \sqrt{60} = \\ = 6 \sqrt{15} - 8 \sqrt{21} + 2 \sqrt{21} - 2 \sqrt{15} \\ = 4 \sqrt{15} - 6 \sqrt{21} [/tex]
[tex]f) - 3 \sqrt{20} \times ( \sqrt{5} + \sqrt{3} ) - 6( \sqrt{15} - 5) = \\ = - 3 \sqrt{100} - 3 \sqrt{60} - 6 \sqrt{15} + 30 = \\ = - 3 \times 10 - 3 \times 2 \sqrt{15} - 6 \sqrt{15} + 30 \\ = - 30 - 6 \sqrt{15} - 6 \sqrt{15} + 30 = - 12 \sqrt{15} [/tex]
