Understanding Cube Roots and Radicals

The video tutorial explains how to multiply radicals, specifically cube roots, by multiplying the radicands when the indices are the same. It demonstrates the process through three examples, showing how to simplify the results using prime factorization and identifying perfect cube factors. The tutorial also covers handling variables within the radicands, emphasizing the importance of simplifying expressions by grouping factors into perfect cubes.

What is the first step when multiplying radicals with the same index?

• Subtract the radicands

• Multiply the radicands

• Divide the radicands

• Add the radicands

What is the prime factorization of 4?

• 2 times 5

• 2 times 3

• 2 times 2

• 3 times 3

In the first example, what is the simplified form of the cube root of 4 times 12?

• Cube root of 48

• 2 times cube root of 6

• Cube root of 24

• 3 times cube root of 8

When multiplying cube roots with coefficients, what should you do with the coefficients?

• Add them

• Multiply them

• Subtract them

• Divide them

What is the prime factorization of 54?

• 3 times 3 times 3

• 2 times 2 times 3

• 2 times 3 times 9

• 2 times 3 times 3 times 3

In the second example, what is the simplified form of 7 cube root 54 times 2 cube root 28?

• 28 cube root 7

• 84 cube root 7

• 56 cube root 7

• 14 cube root 7

What is the product of x^2 times x^5?

• x^10

• x^7

• x^5

• x^9

In the final example, what is the simplified form of the cube root of 9x^2 times 30x^5?

• x^2 cube root of 10x

• 3 cube root of 10x

• 3x cube root of 10x

• 3x^2 cube root of 10x

What is a perfect cube factor of x^7?

• x^3

• x^6

• x^5

• x^4

What is the cube root of 3 times 3 times 3?

• 1

• 27

• 9

• 3