text: +0
  
  # what is the geometric mean of 10 and 30
  
  0
  305
  4
  
  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
  
  ### 20 Online Users
  
  We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details
explanation: The document contains a math question and an answer to this question. The question is "What is the geometric mean of 10 and 30?" and the answer provided is \( \sqrt{10 \times 30} = \sqrt{300} = 10\sqrt{3} \).
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: +0
  
  # what is the geometric mean of 10 and 30
  
  0
  305
  4
  
  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
  
  ### 20 Online Users
  
  We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and an answer to this question. The question is "What is the geometric mean of 10 and 30?" and the answer provided is \( \sqrt{10 \times 30} = \sqrt{300} = 10\sqrt{3} \).
  
  Label: question-and-answer