Multiplying and Simplifying Radical Expressions

This video tutorial introduces the concept of multiplying radical expressions, focusing on radicals with the same index. It explains the process of multiplying coefficients and radicands, followed by simplification. The tutorial provides several examples, demonstrating the use of prime factorization to simplify results. It covers square roots, cube roots, and fourth roots, offering advanced techniques for handling complex expressions.

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

• Subtract the radicands

• Multiply the coefficients

• Divide the radicands

• Add the coefficients

When multiplying the square root of 2 and the square root of 3, what is the resulting expression?

• Square root of 5

• Square root of 1

• Square root of 6

• Square root of 9

In the example of multiplying 3√5 and 4√7, what is the product of the coefficients?

• 12

• 15

• 20

• 7

What is the prime factorization of 15?

• 3 * 5

• 2 * 3

• 2 * 7

• 5 * 5

How do you simplify the cube root of 18 * 60?

• Subtract the numbers, then find the cube root

• Add the numbers, then find the cube root

• Factorize each number separately, then combine

• Find the product first, then factorize

What is the result of multiplying 3√12 and 5√63?

• 15√21

• 30√21

• 45√21

• 60√21

When simplifying the fourth root of 40 * 18, what is the perfect fourth root factor?

• 2

• 3

• 4

• 5

What is the simplified form of -2 * 7 * the fourth root of 40 * 18?

• -14 * the fourth root of 45

• -14 * the fourth root of 90

• -28 * the fourth root of 45

• -28 * the fourth root of 90

In the final example, what is the result of multiplying √6 by -3√6?

• 18

• -18

• 36

• -36

What is the importance of identifying perfect square factors when simplifying radical expressions?

• It helps in adding the expressions

• It allows for easier multiplication

• It simplifies the expression by removing the radical

• It is necessary for dividing the expressions