What is the geometric mean of two positive numbers a and b?
Geometric Mean

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•
Mathematics
•
9th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
The geometric mean is defined as the square root of the product of the two numbers: √(a*b).
2.
FLASHCARD QUESTION
Front
Calculate the geometric mean of 4 and 16.
Back
The geometric mean is √(4*16) = √64 = 8.
3.
FLASHCARD QUESTION
Front
If the geometric mean of x and 9 is 3, what is the value of x?
Back
x = 3^2 / 9 = 1.
4.
FLASHCARD QUESTION
Front
What is the formula for finding the geometric mean of n numbers?
Back
The geometric mean of n numbers is (x1 * x2 * ... * xn)^(1/n).
5.
FLASHCARD QUESTION
Front
Find the geometric mean of 2 and 18.
Back
The geometric mean is √(2*18) = √36 = 6.
6.
FLASHCARD QUESTION
Front
If the geometric mean of 5 and x is 10, what is x?
Back
x = 10^2 / 5 = 20.
7.
FLASHCARD QUESTION
Front
What is the relationship between the arithmetic mean and the geometric mean?
Back
The arithmetic mean is always greater than or equal to the geometric mean for non-negative numbers.
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