Răspuns:
[tex]a) \sqrt{3} ( \sqrt{3} + \sqrt{2} ) - \sqrt{2} ( \sqrt{3} - \sqrt{2} ) = \\ = \sqrt{3} \times \sqrt{3} + \sqrt{3} \times \sqrt{2} - \sqrt{2} \times \sqrt{3} - \sqrt{2} \times ( - \sqrt{2} ) = \\ = 3 + \sqrt{6} - \sqrt{6} + 2 = 5[/tex]
[tex]b)2 \sqrt{2} \times ( \sqrt{18} - \sqrt{50} ) + 4 \sqrt{12} \div \sqrt{3} = \\ = 2 \sqrt{2} \times \sqrt{18} - 2 \sqrt{2} \times \sqrt{50} + 4 \sqrt{4} = \\ = 2 \sqrt{36} - 2 \sqrt{100} + 4 \times 2 = \\ = 2 \times 6 - 2 \times 10 + 8 = 16 - 20 + 8 = - 4 + 8 = 4[/tex]
[tex]c) \sqrt{3} ( \sqrt{2} + 3 \sqrt{3} ) - ( \sqrt{3} + \sqrt{8} ) \times 2 \sqrt{2} = \\ = \sqrt{3} \times \sqrt{2} + \sqrt{3} \times 3 \sqrt{3} - (\sqrt{3} \times 2 \sqrt{2} + \sqrt{8} \times 2 \sqrt{2} ) = \\ = \sqrt{6} + 3 \times 3 - (2 \sqrt{6} + 2 \sqrt{16} ) = \\ = \sqrt{6} + 9 - 2 \sqrt{6} - 2 \times 4 = \\ = - \sqrt{6} + 9 - 8 = - \sqrt{6} + 1[/tex]
[tex]d)(2 \sqrt{6} + \sqrt{54} ) \div \sqrt{6} - (8 \sqrt{5} - \sqrt{45} ) \div \sqrt{5} = \\ = 2 \sqrt{6} \div \sqrt{6} + \sqrt{54} \div \sqrt{6} - (8 \sqrt{5} \div \sqrt{5} - \sqrt{45} \div \sqrt{5} ) = \\ = 2 + \sqrt{9} - (8 - \sqrt{9} ) = \\ = 2 + 3 - (8 - 3) = 5 - 5 = 0[/tex]
