Question 1185706
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Geometric mean of n terms  {{{a[1]}}}, {{{a[2]}}}, . . . , {{{a[n]}}} is,  <U>BY THE DEFINITION</U>,  the root of degree n  of the product of these terms


    {{{GM(a[1], a[2], ellipsis, a[n])}}} = {{{root(n, a[1]*a[2]*ellipsis*a[n])}}}.


In this case, GM(2,4,8,16,32,64) = {{{root(6,2*4*8*16*32*64)}}} = {{{root(6,2^21)}}} = {{{2^3*sqrt(2)}}} = {{{8*sqrt(2)}}} = 11.314  (rounded).    <U>ANSWER</U>
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Solved.


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On Geometric mean see this Wikipedia article


https://en.wikipedia.org/wiki/Geometric_mean