Geometric Mean

Front

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

Back

The geometric mean is defined as the square root of the product of the two numbers: √(a*b).

Front

Calculate the geometric mean of 4 and 16.

Back

The geometric mean is √(4*16) = √64 = 8.

Front

If the geometric mean of x and 9 is 3, what is the value of x?

Back

x = 3^2 / 9 = 1.

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).

Front

Find the geometric mean of 2 and 18.

Back

The geometric mean is √(2*18) = √36 = 6.

Front

If the geometric mean of 5 and x is 10, what is x?

Back

x = 10^2 / 5 = 20.

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.

Front

Calculate the geometric mean of 1 and 25.

Back

The geometric mean is √(1*25) = √25 = 5.

Front

If the geometric mean of a and b is 12, what is the product of a and b?

Back

The product of a and b is 12^2 = 144.

Front

Find the geometric mean of 3 and 27.

Back

The geometric mean is √(3*27) = √81 = 9.