Simplifying Cube Roots and Factors

The video tutorial explains how to simplify cube roots by identifying perfect cube factors through prime factorization. It provides three examples: simplifying the cube root of 54, the cube root of negative 32, and the cube root of 108 with variables. Each example demonstrates the process of breaking down the radicand into its prime factors, identifying perfect cubes, and simplifying the expression.

What is the index of a cube root?

• 4

• 5

• 2

• 3

Which of the following is a perfect cube factor of 54?

• 2

• 3

• 9

• 27

What is the simplified form of the cube root of 54?

• 3 times the cube root of 2

• 2 times the cube root of 3

• 3 times the cube root of 3

• 2 times the cube root of 2

How do you handle the negative sign when simplifying the cube root of negative 32?

• Use negative 1 raised to an odd power

• Use negative 1 raised to an even power

• Treat it as a positive number

• Ignore it

What is the simplified form of the cube root of negative 32?

• Negative 4 times the cube root of 2

• 4 times the cube root of 2

• 2 times the cube root of 4

• Negative 2 times the cube root of 4

What is the prime factorization of 108?

• 2 x 54

• 2 x 3 x 18

• 2 x 2 x 3 x 3 x 3

• 3 x 36

How many factors of x are there in the expression for the cube root of 108?

• 7

• 6

• 8

• 5

What is the simplified form of the cube root of 108?

• 3xy times the cube root of 4x

• 3x^2y times the cube root of 4x

• 3y times the cube root of 4x

• 3x^2 times the cube root of 4x

Which of the following is a perfect cube factor of 108?

• 2

• 3

• 4

• 5

What is the cube root of y^3?

• y^2

• y^4

• y

• y^3