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 9.

Back

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

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 relationship between the arithmetic mean and the geometric mean?

Back

The arithmetic mean is always greater than or equal to the geometric mean for any set of non-negative numbers.

Front

Solve for x: If the geometric mean of x and 16 is 8, what is x?

Back

√(x*16) = 8. Squaring both sides gives x*16 = 64, so x = 4.

Front

What is the geometric mean of 1 and 25?

Back

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

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.

Front

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

Back

The geometric mean of n numbers a1, a2, ..., an is (a1*a2*...*an)^(1/n).

Front

Calculate the geometric mean of 2, 8, and 18.

Back

The geometric mean is (2*8*18)^(1/3) = 48^(1/3) = 3.634.

Front

If the geometric mean of x and 36 is 12, what is x?

Back

√(x*36) = 12. Squaring both sides gives x*36 = 144, so x = 4.