**Middle School Number Sense Lesson 110: Finding the Geometric Mean**

We have already covered finding the arithmetic mean (

**FindMeanAvg**), and this concept is a little different. It appeared

**3 times**this year, with a median placement at

**question # 59**.

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The

**geometric mean**of a set of

**numbers is defined as the**

*n***of the product of the numbers. So the geometric mean of two numbers is the square root of their product, the geometric mean of three numbers is the cube root of their product, etc. On number sense tests, you’ll rarely see a**

*nth root**geometric mean*question involving more than 2 numbers.

**How to Solve:**

- If possible, take the square root of each number and then multiply the results.
- If not, multiply the numbers first and then take the square root of their product.

**Example 1: The positive geometric mean between 4 and 9 is ___**

- √4 =
**2**. √9 =**3**. - 2 x 3 =
**6**.

**Example 2: The positive geometric mean of 16 and 25 is ___**

- √16 =
**4**. √25 =**5**. - 4 x 5 =
**20**.

**Example 3: The positive geometric mean between 40 and 10 is ___**

- 40 x 10 =
**400**. - √400 =
**20**.

**Example 4: The geometric mean of 18 and 50 is ___**

- 18 x 50 =
**900**. - √900 =
**30**.

**Example 5: The geometric mean of 4, 6, and 9 is ___**

- 4 x 6 x 9 =
**216**. - The cube root of 216 is
**6**.

**Example 6:**

**The geometric mean of 5**

^{7}, 5^{11}and 5^{18}is 5^{x}. x = ___1. 5

^{7}x 5

^{11}x 5

^{18}= 5

^{(7 + 11 + 18)}= 5

^{36}.

2. The cube root of 5

^{36}= 5

^{12}, so x =

**12**.

**Here's a free worksheet to help you practice FindMeanGeom:**

findmeangeom.pdf |

**Up Next for Middle School: ConvGalToInch**