Roots

Roots

Let's review square and cube roots

Cubed Roots

In order to find the cubed root of a number:

First, determine what your perfect cubes are.

Second, determine if your perfect cubed match the number under the radical sign.

Third, when the perfect cube is found, determine the base factor and you have your answer.

Multiple Choice

Cubed root of 729

• 7

• 8

• 9

• 11

Fill in the Blanks

What is 11³?

Multiple Choice

In order to find a decimal square root, where do you start?

• You find the square root.

• You solve.

• You change the factor into a decimal.

• You change the decimal into a whole number.

Negative Cubed Roots

Remember, a cubed root can be negative. To find the cubed root of -27, you need to find your perfect cube. 27 is 3 x 3 x 3. When you multiply - 3 x -3 x -3, you will get -27. The answer for this problem is -3.

Multiple Choice

What is the cubed root of - 64?

• 8

• 4

• -8

• -4

Multiple Choice

What is the cubed root of -1000?

• 100

• -100

• -10

• 10

Multiple Choice

Can you have a negative number be found in a square root?

• Yes

• No

Cubed Root of an Equation

For this problem, we have s³ = 125/8. In order to get rid of the exponent of 3, you need to take the cubed root of both sides. Once you do that you will have x= the cubed root of 125/8. When we have this , we will take the cubed root of both numbers. The cubed root of 125 is 5 and cubed root of 8 is 2. The answer will be 5/2 or 2 1/2.

Multiple Choice

What is the inverse operations of x³?

• cubed root

• square root

• multiplication

• division

Multiple Choice

Solve for x: x³ = 64/729

• 4/8

• 8/15

• 1/2

• 4/9

Fill in the Blanks

A gift box is cube shaped and has a volume of 216 cubic inches. Solve to find the length s of one side of the gift box.

Open Ended

A scaled down version of the Pyramid of Giza has a base with an area of 1.44 square feet. The base of the replica is in the shape of a square.

Find the approximate length of each side of the square base in its replica. Write a mathematical argument that can used to defend your solution.