Mastering Multiplication of Radicals with Variables

The video tutorial explains how to multiply radicals containing variables. It emphasizes that the index must be the same for multiplication, and outlines the steps: multiply coefficients, multiply radicands, and simplify the product. Two examples are provided: one with square roots and another with cube roots. The tutorial demonstrates finding prime factorizations to identify perfect square or cube factors for simplification. It also discusses when to use absolute values based on the index and exponent. The video concludes with a summary of the process and encourages viewers to practice the method.

What must be the same when multiplying radicals?

• The radicands

• The variables

• The coefficients

• The index

What is the last step in simplifying the product of radicals?

• Simplify the product

• Multiply the coefficients

• Multiply the radicands

• Find the prime factorization

What is the first step in multiplying the square roots of 18x^3 and 30x^2?

• Simplify the radicands

• Multiply the coefficients

• Find the prime factorization

• Multiply the square roots

What is the prime factorization of 18?

• 2 x 2 x 3

• 3 x 6

• 2 x 9

• 2 x 3 x 3

How do you write x^5 to identify perfect square factors?

• x^4 x x

• x^2 x x^3

• x^3 x x^2

• x^2 x x^2 x x

What is the simplified form of the square root of 18x^3 times the square root of 30x^2?

• 3x^2 x sqrt(15x)

• 6x x sqrt(15x)

• 6x^2 x sqrt(15x)

• 3x x sqrt(15x)

What do you need to check if the index is even and the exponent on a variable is odd?

• The absolute value

• The prime factorization

• The radicand

• The coefficient

What is the prime factorization of 16?

• 2 x 8

• 2 x 2 x 4

• 4 x 4

• 2 x 2 x 2 x 2

How do you write x^4 to identify perfect cube factors?

• x^2 x x^2

• x^3 x x

• x^4

• x^3 x x^2

What is the simplified form of the cube root of 16x^2 times the cube root of 81x^2?

• 6x^2 x cube root(6x)

• 3x x cube root(6x)

• 3x^2 x cube root(6x)

• 6x x cube root(6x)