Question

Calculati media geometrica a numerelor: 
√2 si √8
√12 si √300
3+√5 si 3-√5
11- 6√2 si 11+6√2

Answer 1

$\sqrt{ \sqrt{2} * \sqrt{8} }= \sqrt{  \sqrt{16} }= \sqrt{4}=2$

$\sqrt{ \sqrt{12} * \sqrt{300} } = \sqrt{ \sqrt{3*4}* \sqrt{3*100} } = \sqrt{2 \sqrt{3}*10 \sqrt{3} }=$
$= \sqrt{20 \sqrt{9} } = \sqrt{20*3}= \sqrt{60}$

$\sqrt{(3+ \sqrt{5})(3- \sqrt{5}) }= \sqrt{9-3 \sqrt{5}+3 \sqrt{5}- \sqrt{25} }= \sqrt{9- \sqrt{25} }=$
$= \sqrt{9-5}= \sqrt{4}=2$

$\sqrt{(11-6 \sqrt{2})(11+6 \sqrt{2}) }= \sqrt{121+66 \sqrt{2}-66 \sqrt{2}-36 \sqrt{4} }=$
$= \sqrt{121-36*2}= \sqrt{121-72}= \sqrt{49}=7$