**Middle School Number Sense Lesson 27: Cube Roots**

Cube roots showed up

**9 times**this year--5 times at

**question # 25**and 4 times at # 57. The questions from # 25 were testing memorization of perfect cubes, and the questions from # 57 were testing whether students understand the secret of perfect cubes (discussed last week here).

**Number Dojo Level: 183**

Since this this concept is based on memorization, I won't go into much detail on how it works. I simply will reemphasize the importance of using flash cards (which are available for order on the Worksheets section of this website).

**Example 1: The cube root of 343 is ___**

- The answer is
**7**.

**Example 2: The cube root of 1331 is ___**

- The answer is
**11**

**Example 3: The cube root of -64 is ___**

- Notice the negative sign. The answer is
**-4**.

**Example 4: The cube root of -216 is ___**

- Notice the negative sign. The answer is
**-6**.

The next few examples test your knowledge of

**the secret of perfect cubes**. Take time to review it now (CubesPowers) if you haven't already.

**Rest assured that, unless the question number is a multiple of 10 and has an asterisk next to it, all of your answers will be integers**.

**Example 5: The cube root of 9261 is ___**

- The last digit has to be a
**1**, because 1 x 1 x 1 = 1. (Any number ending in 1, when cubed, also ends in a 1). - The cube root has to be somewhere between 20 & 30, because 20 x 20 x 20 =
**8000**and 30 x 30 x 30 =**27000**. 9261 is found nestled safely between 8000 & 27000. - Therefore, the cube root of 9261 is
**21**.

**Example 6: The cube root of 42875 is ___**

- The last digit has to be a
**5**, because any number ending in 5, when cubed, also ends in a 5. - The cube root has to be somewhere between 30 & 40, because 30 cubed is
**27000**and 40 cubed is**64000**. 42875 is between 27000 and 64000. - Therefore, the cube root of 42875 is
**35**.

**Example 7: The cube root of 148877 is ___**

- The last digit has to be a
**3**, because any number ending in 3, when cubed, ends in a 7. - The cube root has to be somewhere between 50 & 60, because 50 cubed is 125000 and 60 cubed is 216000. 148877 is between 125000 and 216000.
- Therefore, the cube root of 148877 is
**53**.

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

cuberoot.pdf |

**Up Next for Middle School: AddSeqOdd**