SOLUTION: If 0 < a < b, show that a < sqrt{ab} < b. Note: The number sqrt{ab} is called the geometric team of a and b.

Question 1208896: If 0 < a < b, show that a < sqrt{ab} < b.
Note: The number sqrt{ab} is called the geometric team of a and b.

Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!


0 < a < b

Multiply through by a:





Nonnegative square roots are in the same order of inequality as their squares. 
So we take nonnegative square roots:



0 < a < b

Multiply through by b:





Nonnegative square roots are in the same order of inequality as their squares. 
So we take nonnegative square roots:



 and 

Therefore 

Edwin

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