Răspuns:
[tex]a)2 \sqrt{3} \times (2 \sqrt{2} + \sqrt{12} ) - \sqrt{96} = \\ = 4 \sqrt{6} + 4 \sqrt{36} - \sqrt{96} = \\ = 4 \sqrt{6} + 4 \times 6 - \sqrt{16 \times 6} = 4 \sqrt{6} + 24 - 4 \sqrt{6} = 24[/tex]
[tex]b)2 \sqrt{8} \times ( \sqrt{200} - \sqrt{648} + \sqrt{162} ) = \\ = 2 \sqrt{1600} - 2 \sqrt{5184} - 2 \sqrt{1296 } = \\ = 2 \times 40 - 2 \times 72 - 2 \times 36 = \\ = 80 - 144 - 72 = - 64 - 72 = - 136[/tex]
[tex]c)3 \sqrt{20} + 2 \sqrt{5} \times (1 - \sqrt{2} ) - 8 \sqrt{5} + 3 \sqrt{10} = \\ = 3 \times \sqrt{4 \times 5} + 2 \sqrt{5} - 2 \sqrt{10} - 8 \sqrt{5} + 3 \sqrt{10} = \\ = 3 \times 2 \sqrt{5} + 2 \sqrt{5} - 2 \sqrt{10} - 8 \sqrt{5} + 3 \sqrt{10} = \\ = 6 \sqrt{5} + 2 \sqrt{5} - 2 \sqrt{10} - 8 \sqrt{5} - 3 \sqrt{10} = - 5 \sqrt{10} [/tex]
[tex]d) \frac{ \sqrt{6} }{2} \times \frac{ \sqrt{3} }{3} + ( - \frac{2 \sqrt{10} }{5} ) \times \frac{ \sqrt{5} }{4} - \sqrt{56} \div \sqrt{7} = \\ = \frac{ \sqrt{18} }{6} - \frac{2 \sqrt{50} }{20} - \sqrt{8} = \\ = \frac{3 \sqrt{2} }{6} - \frac{2 \times 5 \sqrt{2} }{20} - 2 \sqrt{2} = \\ = \frac{ \sqrt{2} }{2} - \frac{10 \sqrt{2} }{20} - 2 \sqrt{2} = \\ = \frac{ \sqrt{2} }{2} - \frac{ \sqrt{2} }{2} - 2 \sqrt{2} = - 2 \sqrt{2} [/tex]
[tex]e)0.5 \sqrt{24} - \sqrt{3} \times ( \sqrt{2} + 2) + \sqrt{54} \div (3 \sqrt{2} ) = \\ = 0.5 \times 2 \sqrt{6} - \sqrt{6} - 2 \sqrt{3} + 3 \sqrt{6} \div (3 \sqrt{2} ) = \\ = 1\sqrt{6} - 1\sqrt{6} - 2 \sqrt{3} + \sqrt{3} = - \sqrt{3} [/tex]
[tex]f)( - \sqrt{40} - \sqrt{90} + 2 \sqrt{250} ) ^{3} \div ( - \sqrt{3125} ) = \\ = ( - 2 \sqrt{10} - 3 \sqrt{10} + 2 \times 5 \sqrt{10} ) ^{3} \div ( - \sqrt{3125} ) = \\ = ( - 5 \sqrt{10} + 10 \sqrt{10} ) ^{3} \div ( - \sqrt{3125} ) = \\ = {(5 \sqrt{10}) }^{3} \div ( - \sqrt{3125} ) = \\ = {5}^{3} \times ( \sqrt{10} ) ^{3} \div ( - \sqrt{3125} ) = \\ = 125 \times 10 \sqrt{10} \div ( - \sqrt{3125} ) = \\ = 1250 \sqrt{10} \div ( - \sqrt{3125} ) = \\ = 1250 \sqrt{10} \div ( - \sqrt{ {5}^{5} } ) = \\ = 1250 \sqrt{10} \div ( - \sqrt{ {5}^{2} \times {5}^{3} } ) = \\ = 1250 \sqrt{10} \div ( - 5 \sqrt{ {5}^{2} \times 5 } ) = \\ = 1250 \sqrt{10} \div ( - 5 \times 5 \sqrt{5} ) = \\ = 1250 \sqrt{10} \div ( - 25 \sqrt{5} ) = \\ = 50 \sqrt{2} [/tex]
