Question

Calculați media geometrică a numerelor :
$a = \frac{1}{ \sqrt{2} } + 4 \sqrt{2 \: } \: \: si \: b = \sqrt{18} + \sqrt{8 } - \sqrt{32}$
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Answer 1

$a = {}^{ \sqrt{2} )} \frac{1}{ \sqrt{2} } + 4 \sqrt{2} \\ \\ a = \frac{ \sqrt{2} }{2} +{ }^{2)} 4 \sqrt{2} = \frac{ 9\sqrt{2} }{2}$

$b = \sqrt{18} + \sqrt{8} - \sqrt{32} \\ \\ b = \sqrt{3 {}^{2} \times 2 } + \sqrt{ {2}^{3}} - \sqrt{ {2}^{5} } \\ \\ b = 3 \sqrt{2} + 2 \sqrt{2} - 4 \sqrt{2} = \sqrt{2}$

$mg = \sqrt{a \times b} \\ \\ mg = \sqrt{ \frac{9 \sqrt{2} }{2} \times \sqrt{2} } = \sqrt{ \frac{9 \times 2}{2} } \\ \\ mg = \sqrt{9} = 3$