Răspuns:
[tex]1) \sqrt{25} - \sqrt{9} + \sqrt{1} = 5 - 3 + 1 = 3 \\ 2 \times \sqrt{100} - \sqrt{36} - 3 \times ( \sqrt{25} + \sqrt{16} ) \div \sqrt{36} = \\ = 2 \times 10 - 6 - 3 \times (5 + 4) \div 6 = \\ = 20 - 6 - 3 \times 9 \div 6 = \\ = 20 - 6 - 27 \div 6 = 20 - 6 - \frac{27}{6} = 20 - 6 - \frac{9}{2} = \frac{40}{2} - \frac{12}{2} - \frac{9}{2} = \frac{17}{2} [/tex]
[tex]2)2 \sqrt{5} = \sqrt{ {2}^{2} \times 5} = \sqrt{4 \times 5} = \sqrt{20} \\ 4 \sqrt{2} = \sqrt{ {4}^{2} \times 2 } = \sqrt{32} \\ 3 \sqrt{2} = \sqrt{ {3}^{2} \times 2 } = \sqrt{9 \times 2} = \sqrt{18} \\ 6 = \sqrt{ {6}^{2} } = \sqrt{36} \\ \sqrt{18} . \sqrt{20} . \sqrt{32} . \sqrt{36} [/tex]
[tex]3) \sqrt{216} = \sqrt{ {6}^{3} } = \sqrt{ {6}^{2} \times 6 } = \sqrt{ {6}^{2} } \times \sqrt{6} = 6 \sqrt{6} \\ \sqrt{ {3}^{5} \times {2}^{7} } = \sqrt{ {3}^{5} } \times \sqrt{ {2}^{7} } = \sqrt{ {3}^{4 + 1} } \times \sqrt{ {2}^{6 + 1} } = \sqrt{ {3}^{4} \times 3 } \times \sqrt{ {2}^{6} \times 2} = \sqrt{ {3}^{4} } \times \sqrt{3} \times \sqrt{ {2}^{6} } \times \sqrt{2} = \sqrt{( {3}^{2}) ^{2} } \times \sqrt{3} \times \sqrt{( {2}^{3}) ^{2} } \times \sqrt{2} = {3}^{2} \times \sqrt{3} \times {2}^{3} \times \sqrt{2} = 9 \sqrt{3} \times 8 \sqrt{2} = 72 \sqrt{6} [/tex]
[tex] \sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4 \sqrt{5} \\ \sqrt{800} = \sqrt{8 \times 100} = \sqrt{8} \times \sqrt{100} = \sqrt{4 \times 2} \times 10 = \sqrt{4} \times \sqrt{2} \times 10 = 2 \sqrt{2} \times 10 = 20 \sqrt{2} [/tex]
[tex]4)2 \sqrt{2} - ( + 2) - ( - 2 \sqrt{2} ) + ( - 5) = 2 \sqrt{2} - 2 + 2 \sqrt{2} - 5 = 4 \sqrt{2} - 7[/tex]
[tex] \sqrt{ {2}^{3} } + \sqrt{ {2}^{5} } + \sqrt{ {2}^{7} } = \sqrt{ {2}^{2} \times 2} + \sqrt{ {2}^{4} \times 2 } + \sqrt{ {2}^{6} \times 2 } = 2 \sqrt{2} + \sqrt{16} \times \sqrt{2} + \sqrt{64} \times \sqrt{2} = 2 \sqrt{2} + 4 \sqrt{2} + 8 \sqrt{2} = 14 \sqrt{2} [/tex]
[tex](3 \sqrt{5} ) \times ( - 2 \sqrt{5}) = - 6 \sqrt{25} = - 6 \times 5 = - 30[/tex]
[tex] - 40 \sqrt{6} \div 5 \sqrt{3} = - 8 \sqrt{2} [/tex]
[tex] {( - 3 \sqrt{2} })^{2} = - 3 \sqrt{2} \times ( - 3 \sqrt{2} ) = 9 \sqrt{4} = 9 \times 2 = 18[/tex]
[tex] \sqrt{3} ( \sqrt{2} + \sqrt{6} ) = \sqrt{3} \times \sqrt{2} + \sqrt{3} \times \sqrt{6} = \sqrt{6} + \sqrt{18} = \sqrt{6} + \sqrt{9 \times 2} = \sqrt{6} + 3 \sqrt{2} [/tex]
[tex] \sqrt{14} \div \sqrt{2} - 3 \sqrt{7} = \sqrt{7} - 3 \sqrt{7} = - 2 \sqrt{7} [/tex]
[tex]5) \frac{2}{ \sqrt{5} } = \frac{2 \sqrt{5} }{ \sqrt{5} \times \sqrt{5} } = \frac{2 \sqrt{5} }{5} [/tex]
[tex] \frac{2 \sqrt{3} }{ \sqrt{5} } = \frac{2 \sqrt{15} }{5} [/tex]
[tex]a = 3 \sqrt{2} + 1 \\ b = 3 \sqrt{2} - 1 \\ ma = \frac{3 \sqrt{2} + 1 + 3 \sqrt{2} - 1 }{2} = \frac{6 \sqrt{2} }{2} = 3 \sqrt{2} [/tex]
