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

How do you calculate the geometric mean of 4 and 9?

Back

The geometric mean of 4 and 9 is √(4*9) = √36 = 6.

Front

What is the formula for finding the geometric mean of n numbers?

Back

The geometric mean of n numbers x1, x2, ..., xn is given by (x1 * x2 * ... * xn)^(1/n).

Front

If the geometric mean of two numbers is 8 and one of the numbers is 4, what is the other number?

Back

Let the other number be x. Then, √(4*x) = 8. Squaring both sides gives 4*x = 64, so x = 16.

Front

What is the geometric mean of 6 and 8?

Back

The geometric mean of 6 and 8 is √(6*8) = √48 = 4√3.

Front

If x = 4, what is the geometric mean of x and 16?

Back

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

Front

What is the geometric mean of 1 and 25?

Back

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

Front

How do you find the geometric mean of three numbers: 2, 8, and 18?

Back

The geometric mean is (2*8*18)^(1/3) = 12.

Front

What is the geometric mean of 3 and 12?

Back

The geometric mean of 3 and 12 is √(3*12) = √36 = 6.

Front

If the geometric mean of two numbers is 10 and one of the numbers is 5, what is the other number?

Back

Let the other number be y. Then, √(5*y) = 10. Squaring both sides gives 5*y = 100, so y = 20.