[tex]a)ma = \frac{6 + 54}{2} = \frac{60}{2} = 30 \\ mg = \sqrt{6 \times 54 } = radical din 324=18 \\ mh = \frac{2 \times 6 \times 54}{6 + 54} = \frac{648}{60} = 10.8[/tex]
[tex]b)ma = \frac{ \frac{1}{4} + \frac{1}{9} }{2} = \frac{ \frac{9}{36} + \frac{4}{36} }{2} = \frac{ \frac{13}{36} }{2} = \frac{13}{36} \times \frac{1}{2} = \frac{13}{72} \\ mg = \sqrt{ \frac{1}{4} \times \frac{1}{9} } = \sqrt{ \frac{1}{36} } = \sqrt{ \frac{1}{ {6}^{2} } } = \frac{1}{6} \\ mh = \frac{2 \times \frac{1}{4} \times \frac{1}{9} }{ \frac{1}{4} + \frac{1}{9} } = \frac{ \frac{2}{36} }{ \frac{13}{36} } = \frac{2}{36} \times \frac{36}{13} = \frac{2}{13} [/tex]
[tex]c)ma = \frac{5 + 7.2}{2} = \frac{12.2}{2} = 6.1 \\ mg = \sqrt{5 \times 7.2} = \sqrt{36 } = 6 \\ mh = \frac{2 \times 5 \times 7.2}{5 + 7.2} = \frac{72}{12.2} = 5.9[/tex]
[tex]d)ma = \frac{25 \sqrt{3} + 12 \sqrt{3} }{2} = \frac{37 \sqrt{3} }{2} = 18.5 \sqrt{3} \\ mg = \sqrt{25 \sqrt{ 3 } \times 12 \sqrt{3} } = \sqrt{25 \times 12 \times 3} = \sqrt{900} = 30 \\ mh = \frac{2 \times 25 \sqrt{3} \times 12 \sqrt{3} }{25 \sqrt{3} + 12 \sqrt{3} } = \frac{1800}{37 \sqrt{3} } = \frac{1800 \sqrt{3} }{111} [/tex]
[tex]e)ma = \frac{ \sqrt{2} + \sqrt{8} }{2} = \frac{ \sqrt{2} + \sqrt{ {2}^{3} } }{2} =\frac{ \sqrt{2} + 2 \sqrt{2} }{2} = \frac{3 \sqrt{2} }{2} \\ mg = \sqrt{ \sqrt{2} \times \sqrt{8} } = \sqrt{ \sqrt{2} \times 2 \sqrt{2} } = \sqrt{2 \times 2 } = \sqrt{4} = 2 \\ mh = \frac{2 \times \sqrt{2} \times \sqrt{8} }{ \sqrt{2} + \sqrt{8} } = \frac{2 \times \sqrt{2} \times 2 \sqrt{2} }{ \sqrt{2} + 2 \sqrt{2} } = \frac{8}{3 \sqrt{2} } = \frac{8 \sqrt{2} }{6} = \frac{4 \sqrt{2} }{3} [/tex]