Multiplying and Simplifying Radicals

This video tutorial covers the multiplication of radical expressions with variables. It begins with an introduction to the concept, followed by several examples demonstrating the process of multiplying radicals, including square roots and cube roots. The tutorial emphasizes the importance of prime factorization in simplifying the expressions and provides step-by-step guidance on handling complex radicals. By the end, viewers will understand how to multiply and simplify radical expressions with variables effectively.

What is the first step in multiplying two radical expressions with the same index?

• Subtract the radicands

• Add the terms outside the radicals

• Multiply the terms outside the radicals

• Divide the radicands

When multiplying the square root of 2x and the square root of 3xy, what is the product of the radicands?

• 6x^2y

• 5xy

• 6xy

• 5x^2y

In the example with the square root of 21x^2y and the square root of 28xy^3, what is the simplified form of the expression?

• 14xy^2√3x

• 14x^2y√3

• 14xy^3√3x

• 14x^2y^2√3

What is the prime factorization of 28 used in the example with square roots?

• 2 x 3 x 7

• 3 x 7

• 4 x 7

• 2 x 2 x 7

When multiplying cube roots, what is the key difference compared to square roots?

• Looking for groups of three equal factors

• Adding the radicands

• Subtracting the radicands

• Looking for groups of two equal factors

In the cube root example, what is the simplified form of the expression involving 4a^2b^2 and 12ab^3?

• 2ab√6

• 2ab^2√6b

• 2a^2b^2√6

• 2ab√6b^2

What is the prime factorization of 12 used in the cube root example?

• 2 x 2 x 2

• 2 x 3

• 3 x 4

• 2 x 2 x 3

In the final example, what is the product of the terms outside the square roots?

• 5xy

• 10xy

• 15xy

• 20xy

What is the simplified form of the expression involving 2xy√8x^3y and 5√6xy^2?

• 40x^2y^2√3y

• 30x^3y^2√3y

• 40x^3y^2√3y

• 30x^2y^2√3y

What is the prime factorization of 8 used in the final example?

• 2 x 2

• 3 x 3

• 2 x 3

• 2 x 2 x 2