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  # what is the geometric mean of 10 and 30
  
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  what is the geometric mean of 10 and 30
  
  Guest Feb 14, 2015
  
  #3
  +26399
  +10
  
  The geometric mean only applies to positive numbers.
  
  It has a geometric interpretation.  Image a rectangle with sides 10 and 30.  It has an area of 300.  A square of side √(10*30), i.e. one with side lengths equal to the geometric mean of the two rectangle lengths, has the same area.
  
  Similarly, for higher order geometric means. e.g. a cuboid with side lengths u, v and w has the same volume as a cube with side lengths 3√(u*v*w), etc.
  
  .
  
  Alan  Feb 14, 2015
  Sort:
  
  #1
  +80875
  +10
  
  The geometric mean of N numbers is just the Nth root of their product.....so, since we have two numbers, we have....
  
  √(10 * 30) = √300 = 10√3
  
  CPhill  Feb 14, 2015
  #2
  +91436
  +5
  
  SO
  
  The geometric mean of 7,6,8 and 2
  
  is it   $$\sqrt[4]{7*6*8*2}$$
  
  $${\left({\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{2}}\right)}^{\left({\mathtt{0.25}}\right)} = {\mathtt{5.091\: \!459\: \!790\: \!043\: \!661}}$$
  
  what happen if there is negative numbers?
  
  Melody  Feb 14, 2015
  #3
  +26399
  +10
  
  The geometric mean only applies to positive numbers.
  
  It has a geometric interpretation.  Image a rectangle with sides 10 and 30.  It has an area of 300.  A square of side √(10*30), i.e. one with side lengths equal to the geometric mean of the two rectangle lengths, has the same area.
  
  Similarly, for higher order geometric means. e.g. a cuboid with side lengths u, v and w has the same volume as a cube with side lengths 3√(u*v*w), etc.
  
  .
  
  Alan  Feb 14, 2015
  #4
  +91436
  0
  
  Thanks Alan
  
  Melody  Feb 15, 2015
  
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