Răspuns:
[tex]a)5 \sqrt{3} \times 2 \sqrt{3} + 3 \sqrt{2} \times \sqrt{2} - 2 \sqrt{5} \times ( - 2 \sqrt{5} ) = 10 \times 3 + 3 \times 2 + 4 \times 5 = 30 + 6 + 20 = 56[/tex]
[tex]b) \sqrt{3} \times ( \sqrt{3} + \sqrt{2} ) + \sqrt{2} \times ( \sqrt{2} - \sqrt{6} ) + \sqrt{6} \times ( \sqrt{2} - 1) = \sqrt{3} \times \sqrt{3} + \sqrt{3} \times \sqrt{2} + \sqrt{2} \times \sqrt{2} + \sqrt{2} \times ( - \sqrt{6} ) + \sqrt{6} \times \sqrt{2} - \sqrt{6} = \\ = 3 + \sqrt{6} + 2 - \sqrt{12} + \sqrt{12} - \sqrt{6} = \\ = 5[/tex]
[tex]c) \sqrt{2} ( \sqrt{3} + \sqrt{2} ) - \sqrt{5} ( \sqrt{3} - \sqrt{5} ) + \sqrt{3 } ( \sqrt{5} - \sqrt{2} ) = \\ = \sqrt{2} \times \sqrt{3} + \sqrt{2} \times \sqrt{2} - \sqrt{5} \times \sqrt{3} - \sqrt{5} \times ( - \sqrt{5} ) + \sqrt{3} \times \sqrt{5} + \sqrt{ 3} \times ( - \sqrt{2} ) \\ = \sqrt{6} + 2 - \sqrt{15} + 5 + \sqrt{15} - \sqrt{6} = \\ = 2 + 5 = 7[/tex]
[tex]d)2 \sqrt{2} ( \sqrt{2} + 1) + 3 \sqrt{3} ( \sqrt{3} - 1) - \sqrt{6} ( \sqrt{6} - 1) = \\ = 2 \sqrt{2} \times \sqrt{2} + 2 \sqrt{2} \times 1 + 3 \sqrt{3} \times \sqrt{3} + 3 \sqrt{3} \times ( - 1) - \sqrt{6} \times \sqrt{6} - \sqrt{6} \times ( - 1) = \\ = 2 \times 2 + 2 \sqrt{2} + 3 \times 3 - 3 \sqrt{3} - 6 + \sqrt{6} \\ = 4 + 2 \sqrt{2} + 9 - 3 \sqrt{3} - 6 + \sqrt{6} \\ = 2 \sqrt{2} - 3 \sqrt{3} + \sqrt{6} + 7[/tex]
