8.1 Geometric Mean Practice

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

6

Front

Calculate the geometric mean of 2 and 25.

Back

5√2

Front

Calculate the geometric mean of 5 and 8.

Back

2√10

Front

In a right triangle, what is the relationship between the altitude to the hypotenuse and the segments it creates?

Back

The altitude to the hypotenuse creates two segments that are proportional to the lengths of the other two sides of the triangle.

Front

If the geometric mean of x and 16 is 8, what is the value of x?

Back

x = 4.

Front

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

Back

The geometric mean of n numbers is the n-th root of the product of the numbers: (x1 * x2 * ... * xn)^(1/n).

Front

Find the geometric mean of 1 and 100.

Back

10.

Front

In a right triangle, if the lengths of the legs are 6 and 8, what is the length of the hypotenuse?

Back

10 (using the Pythagorean theorem).

Front

What is the geometric mean of 3 and 12?

Back

6.