Simplifying Cube Roots: Techniques and Examples

What are the two methods discussed for simplifying cube roots?

• Using estimation and prime factorization

• Using long division and prime factorization

• Finding factors that are perfect cubes and using prime factorization

• Finding factors that are perfect squares and using prime factorization

Which of the following is a perfect cube?

• 16

• 45

• 50

• 27

What is the simplified form of the cube root of 48 using perfect cube factors?

• 3 times the cube root of 6

• 2 times the cube root of 6

• 4 times the cube root of 3

• 6 times the cube root of 2

Which of the following is a factor of 250 that is a perfect cube?

• 10

• 125

• 25

• 50

What is the simplified form of the cube root of 250 using perfect cube factors?

• 5 times the cube root of 10

• 5 times the cube root of 2

• 2 times the cube root of 5

• 10 times the cube root of 5

What is the first step in simplifying cube roots using prime factorization?

• Estimating the cube root

• Finding the least common multiple

• Breaking down the number into prime factors

• Finding the greatest common divisor

What is the prime factorization of 48?

• 2 x 2 x 2 x 3 x 3

• 2 x 2 x 3 x 3

• 2 x 2 x 2 x 2 x 2

• 2 x 2 x 2 x 2 x 3

What is the simplified form of the cube root of 48 using prime factorization?

• 3 times the cube root of 6

• 2 times the cube root of 6

• 4 times the cube root of 3

• 6 times the cube root of 2

What is the prime factorization of 250?

• 2 x 5 x 5 x 5

• 2 x 5 x 5 x 10

• 2 x 2 x 5 x 5

• 2 x 2 x 2 x 5

What is the simplified form of the cube root of 250 using prime factorization?

• 5 times the cube root of 10

• 10 times the cube root of 5

• 5 times the cube root of 2

• 2 times the cube root of 5