Răspuns:
[tex]4)a)x = \frac{2 \sqrt{24} }{ \sqrt{54} - \sqrt{2}( \sqrt{27} - \sqrt{6}) } \times \sqrt{2} \\ x = \frac{2 \times \sqrt{4 \times 6} }{ \sqrt{9 \times 6} - \sqrt{2}( \sqrt{9 \times 3} - \sqrt{6}) } \times \sqrt{2} \\ x = \frac{2 \times \sqrt{4} \times \sqrt{6} }{ \sqrt{9} \times \sqrt{6} - \sqrt{2}( \sqrt{9} \times \sqrt{3} - \sqrt{6} ) } \times \sqrt{2} \\ x = \frac{2 \times 2 \times \sqrt{6} }{3 \times \sqrt{6} - \sqrt{2}(3 \times \sqrt{3} - \sqrt{6}) } \times \sqrt{2} \\ x = \frac{4 \sqrt{6} }{3 \sqrt{6} - 3 \sqrt{6} + \sqrt{12} } \times \sqrt{2} \\ x = \frac{4 \sqrt{6} }{ \sqrt{4 \times 3} } \times \sqrt{2} \\ x = \frac{4 \sqrt{6} }{ \sqrt{4} \times \sqrt{3} } \times \sqrt{2} \\ x = \frac{4 \sqrt{6} }{2 \sqrt{3} } \times \sqrt{2} \\ x = 4 \sqrt{6} \div 2 \sqrt{3} \times \sqrt{2} \\ x = 2 \sqrt{2} \times \sqrt{2 } \\ x = 2 \sqrt{4} = 2 \times 2 = 4[/tex]
[tex]b)y = \sqrt{147} ( \frac{1}{ \sqrt{3} } + \frac{1}{ \sqrt{7} } ) + \sqrt{28} \times ( \frac{1}{ \sqrt{7} } - \frac{ \sqrt{3} }{2} ) \\ y = \frac{ \sqrt{147} }{ \sqrt{3} } + \frac{ \sqrt{147} }{ \sqrt{7} } + \frac{ \sqrt{28} }{ \sqrt{7} } - \frac{ \sqrt{84} }{2} \\ y = \frac{ \sqrt{49} }{1} + \frac{ \sqrt{21} }{1} + \frac{ \sqrt{4} }{1} - \frac{ \sqrt{4 \times 21} }{2} \\ y = 7 + \sqrt{21} + 2 - \frac{ \sqrt{4} \times \sqrt{21} }{2} \\ y = 9 + \sqrt{21} - \frac{2 \sqrt{21} }{2} \\ y = 9 + \sqrt{21} - \sqrt{21} \\ y = 9[/tex]
[tex]mg = \sqrt{x \times y} = \sqrt{4 \times 9} = \sqrt{36} = 6[/tex]
[tex]5)a)x = 3 \sqrt{2} ( \sqrt{50} + \sqrt{72} - \sqrt{200} ) \\ x = 3 \sqrt{2} ( \sqrt{25 \times 2} + \sqrt{36 \times 2} - \sqrt{100 \times 2} ) \\ x = 3 \sqrt{2} ( \sqrt{25} \times \sqrt{2} + \sqrt{36} \times \sqrt{2} - \sqrt{100} \times \sqrt{2} ) \\ x = 3 \sqrt{2} (5 \sqrt{2} + 6 \sqrt{2} - 10 \sqrt{2} ) \\ x = 3 \sqrt{2} \times \sqrt{2} = 3 \sqrt{4} = 3 \times 2 = 6[/tex]
[tex]b)y = ( \frac{1}{3 \sqrt{3} } + \frac{1}{2 \sqrt{3} } ) \times \sqrt{300} \div \frac{1}{3 \sqrt{36} } \\ y = ( \frac{ \sqrt{300} }{3 \sqrt{3} } + \frac{ \sqrt{300} }{2 \sqrt{3} } ) \times 3 \sqrt{36} \\ y = ( \frac{ \sqrt{100} }{3} + \frac{ \sqrt{100} }{2} ) \times 3 \sqrt{36} \\ y = ( \frac{10}{3} + \frac{10}{2} ) \times 3 \times 6 \\ y = ( \frac{20}{6} + \frac{30}{6} ) \times 18 \\ y = \frac{50}{6} \times 18 \\ y = 50 \times 3 = 150 \\ mg = \sqrt{x \times y} = \sqrt{6 \times 150} = \sqrt{900} = 30[/tex]
