Explicație pas cu pas:
[tex]a)3 \sqrt{50} - \sqrt{180} - \sqrt{18} + \sqrt{45} = \\ \\ 3 \times 5 \sqrt{2} - 6 \sqrt{5} - 3 \sqrt{2} + 3 \sqrt{5} = \\ \\ 15 \sqrt{2} - 6 \sqrt{5} - 3 \sqrt{2} + 3 \sqrt{5} = \\ \\ (15 \sqrt{2} - 3 \sqrt{2}) + ( - 6 \sqrt{5} + 3 \sqrt{5}) = \\ \\ 12 \sqrt{2} - 3 \sqrt{5} [/tex]
[tex]b)5 \sqrt{27} - \sqrt{125} + \sqrt{80} - \sqrt{12} = \\ \\ 5 \times 3 \sqrt{3} - 5 \sqrt{5} + 4 \sqrt{5} - 2 \sqrt{3} = \\ \\ 15 \sqrt{3} - 5 \sqrt{5} + 4 \sqrt{5} - 2 \sqrt{3} = \\ \\ (15 \sqrt{3} - 2 \sqrt{3}) + ( - 5 \sqrt{5} + 4 \sqrt{5}) = \\ \\ 13 \sqrt{3} - \sqrt{5} [/tex]
[tex]c) \sqrt{24} - 4 \sqrt{45} + 3 \sqrt{54} - 2 \sqrt{80} = \\ \\ 2 \sqrt{6} - 4 \times 3 \sqrt{5} + 3 \times 3 \sqrt{6} - 2 \times 4 \sqrt{5} = \\ \\ 2 \sqrt{6} - 12 \sqrt{5} + 9 \sqrt{6} - 8 \sqrt{5} = \\ \\ (2 \sqrt{6} + 9 \sqrt{6}) + ( - 12 \sqrt{5} - 8 \sqrt{5}) = \\ \\ 11 \sqrt{6} - 20 \sqrt{5} [/tex]
[tex]d) \sqrt{98} - \sqrt{96} - 3 \sqrt{150} - 7 \sqrt{50} = \\ \\ 7 \sqrt{2} - 4 \sqrt{6} - 3 \times 5 \sqrt{6} - 7 \times 5 \sqrt{2} = \\ \\ 7 \sqrt{2} - 4 \sqrt{6} - 15 \sqrt{6} - 35 \sqrt{2} = \\ \\ (7 \sqrt{2} - 35 \sqrt{2}) + ( - 4 \sqrt{6} - 15 \sqrt{6}) = \\ \\ - 28 \sqrt{2} - 19 \sqrt{6} [/tex]
[tex]e) \sqrt{108} - 8 \sqrt{175} - 5 \sqrt{48} + \sqrt{63} = \\ \\ 6 \sqrt{3} - 8 \times 5 \sqrt{7} - 5 \times 4 \sqrt{3} + 3 \sqrt{7} = \\ \\ 6 \sqrt{3} - 40 \sqrt{7} - 20 \sqrt{3} + 3 \sqrt{7} = \\ \\ (6 \sqrt{3} - 20 \sqrt{3}) + ( - 40 \sqrt{7} + 3 \sqrt{7}) = \\ \\ - 14 \sqrt{3} - 37 \sqrt{7} [/tex]
[tex]f) - \sqrt{242} + 7 \sqrt{50} - 3 \sqrt{28} + \sqrt{63} = \\ \\ - 11 \sqrt{2} + 7 \times 5 \sqrt{2} - 3 \times 2 \sqrt{7} + 3 \sqrt{7} = \\ \\ - 11 \sqrt{2} + 35 \sqrt{2} - 6 \sqrt{7} + 3 \sqrt{7} = \\ \\ ( - 11 \sqrt{2} + 35 \sqrt{2}) + ( - 6 \sqrt{7} + 3 \sqrt{7}) = \\ \\ 24 \sqrt{2} - 3 \sqrt{7} [/tex]
