Explicație pas cu pas:
6)
[tex]a = \sqrt{5} \times (4 \sqrt{2} - 3 \sqrt{5}) - 2(2 \sqrt{10} + 3) \\ \\ a = 4 \sqrt{10} - 15 - (4 \sqrt{10} + 6) \\ \\ a = 4 \sqrt{10} - 15 - 4 \sqrt{10} - 6 \\ \\ a = (4 \sqrt{10} - 4 \sqrt{10}) + ( - 15 - 6) \\ \\ a = - 21 [/tex]
[tex]b = 2 \sqrt{7} \times (3 - \sqrt{3}) + 2(4 + \sqrt{21}) - 6 \sqrt{7} \\ \\ b = 6 \sqrt{7} - 2 \sqrt{21} + 8 + 2 \sqrt{21} - 6 \sqrt{7} \\ \\ b = (6 \sqrt{7} - 6 \sqrt{7}) + ( - 2 \sqrt{21} + 2 \sqrt{21}) + 8 \\ \\ b = 8 [/tex]
[tex]c = \sqrt{12} \times ( \sqrt{32} - 3 \sqrt{3}) - 4(7 + 2 \sqrt{6}) \\ \\ c = 2 \sqrt{3}(4 \sqrt{2} - 3 \sqrt{3}) - 4(7 + 2 \sqrt{6}) \\ \\ c = 8 \sqrt{6} - 18 - (28 + 8 \sqrt{6}) \\ \\ c = 8 \sqrt{6} - 18 - 28 - 8 \sqrt{6} \\ \\ c = (8 \sqrt{6} - 8 \sqrt{6}) + ( - 18 - 28) \\ \\ c = - 46 [/tex]
[tex]d = \sqrt{48} \times ( \sqrt{8} - \sqrt{3}) - 2 \sqrt{2} \times (4 \sqrt{3} - \sqrt{2}) \\ \\ d = 4 \sqrt{3}(2 \sqrt{2} - \sqrt{3}) - 2 \sqrt{2}(4 \sqrt{3} - \sqrt{2}) \\ \\ d = 8 \sqrt{6} - 12 - (8 \sqrt{6} - 4) \\ \\ d = 8 \sqrt{6} - 12 - 8 \sqrt{6} + 4 \\ \\ d = (8 \sqrt{6} - 8 \sqrt{6}) + ( - 12 + 4) \\ \\ d = - 8 [/tex]
7)
[tex]a)4 \times ( \sqrt{5} - 2 \sqrt{2}) + 3(7 \sqrt{5} - 4 \sqrt{2}) - 7( \sqrt{2} - 3 \sqrt{5}) = \\ \\ 4 \sqrt{5} - 8 \sqrt{2} + 21 \sqrt{5} - 12 \sqrt{2} - (7 \sqrt{2} - 21 \sqrt{5}) = \\ \\ 4 \sqrt{5} - 8 \sqrt{2} + 21 \sqrt{5} - 12 \sqrt{2} - 7 \sqrt{2} + 21 \sqrt{5} = \\ \\ (4 \sqrt{5} + 21 \sqrt{5} + 21 \sqrt{5}) + ( - 8 \sqrt{2} - 12 \sqrt{2} - 7 \sqrt{2}) = \\ \\ 46 \sqrt{5} - 27 \sqrt{2} [/tex]
[tex]b) \sqrt{63} - 3(2 \sqrt{7} - 4 \sqrt{3}) + 4(2 \sqrt{3} + 5 \sqrt{7}) = \\ \\ 3 \sqrt{7} - (6 \sqrt{7} - 12 \sqrt{3}) + 8 \sqrt{3} + 20 \sqrt{7} = \\ \\ 3 \sqrt{7} - 6 \sqrt{7} + 12 \sqrt{3} + 8 \sqrt{3} + 20 \sqrt{7} = \\ \\ (3 \sqrt{7} - 6 \sqrt{7} + 20 \sqrt{7}) + ( - 12 \sqrt{3} + 8 \sqrt{3}) = \\ \\ 17 \sqrt{7} + 20 \sqrt{3} [/tex]
