Question

1. Find the geometric mean of 4 and 10.

A. 20
B. 7
C. √14
D. 2√10

2. Find the geometric mean of 3 and 48.

A. 12
B. 25.5
C. √51
D. 22.5

3. Find the geometric mean of 5 and 125.

A. 65
B. 25
C. 2√30
D. √130

4. Suppose the altitude to the hypotenuse of a right triangle bisects the hypotenuse. How does the length of the altitude compare with the lengths of the segments of the hypotenuse?

A. The length of the altitude is equal to twice the length of one of the segments of the hypotenuse.
B. The length of the altitude is equal to half the length of one of the segments of the hypotenuse.
C. The length of the altitude is equal to the length of one of the segments of the hypotenuse.
D. The length of the altitude is equal to the sum of the lengths of the segments of the hypotenuse.

5. What is the geometric mean of a and b? (There's no picture or any caption, just the question)

A. a + b
--------
2
B. a - b
---------
2
C. √a + b
D. √ab

Answer 1

Explanation:

The geomtric mean of
`N` numbers is the
`N`-th root of all numbers multiplied together:

`\sqrt[N]{A_(1) * A_(2) * ... * A_(N)}`

1. Answer below:

`√(4 * 10)`

`√(40)`

`2√(10)`

2. Answer below:

`√(3 * 48)`

`√(144)`

`12`

3. Answer below:

`√(5 * 125)`

`√(625)`

`25+`

4. C

5. See explanation at the beginning: D