Understanding Radical Multiplication

The video tutorial explains how to multiply radicals with the same index by multiplying their coefficients and radicands. It provides examples of multiplying square roots and cube roots, demonstrating the process of simplification using prime factorization. The tutorial emphasizes identifying perfect square and cube factors to simplify the products.

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

• Add the coefficients

• Multiply the coefficients

• Subtract the radicands

• Divide the radicands

In the example of multiplying 3√2 and 5√6, what is the product of the coefficients?

• 10

• 15

• 18

• 8

What is the prime factorization of 6 used in the example?

• 2 x 5

• 2 x 2

• 3 x 3

• 2 x 3

After simplifying the product of 3√2 and 5√6, what is the final result?

• 30√6

• 15√6

• 15√3

• 30√3

When multiplying cube roots, what is the first step?

• Subtract the radicands

• Multiply the coefficients

• Divide the radicands

• Add the coefficients

In the example of multiplying -4∛9 and 2∛9, what is the product of the coefficients?

• -6

• -8

• -10

• -12

What is the prime factorization of 9 used in the cube root example?

• 3 x 5

• 2 x 3

• 3 x 3

• 2 x 2

After simplifying the product of -4∛9 and 2∛9, what is the final result?

• -16∛3

• -24∛3

• -32∛3

• -40∛3

What is the purpose of using prime factorization in simplifying radical products?

• To add the coefficients

• To identify perfect square or cube factors

• To find the sum of the radicands

• To divide the coefficients

What is the result of multiplying -4∛9 and 2∛9 before simplification?

• -8∛3

• -8∛9

• -8∛27

• -8∛81