Radical Expressions and Simplification

The video tutorial explains how to multiply binomials containing radicals. It begins with a review of the rules for multiplying radicals, emphasizing the need for the same index and the multiplication of coefficients and radicands. The tutorial introduces the concept of double distribution, often referred to as FOIL, to multiply two binomials. Two examples are provided: the first demonstrates the process with simpler radicals, while the second involves more complex radicals. Each example includes detailed steps for distributing terms, simplifying radicals, and combining like terms. The tutorial concludes with a simplified expression for each example.

What must be the same when multiplying radicals?

• The radicands

• The indices

• The exponents

• The coefficients

What is another name for the method of multiplying two binomials?

• Radical Multiplication

• Foiling

• Single Distribution

• Triple Distribution

In the first example, what is the result of multiplying the square root of 3 by itself?

• Square root of 6

• 3

• 6

• Square root of 9

How do you combine like radicals?

• Subtract the coefficients

• Divide the radicands

• Multiply the coefficients

• Add the radicands

What is the simplified form of 3 squared?

• 12

• 3

• 9

• 6

In the second example, what is the first step in the distribution process?

• Distribute 3 square root 2

• Multiply the coefficients

• Combine like terms

• Distribute square root 5

What is the result of multiplying square root 5 by square root 2?

• 5

• 10

• Square root 10

• 2

What is the simplified form of -2 times the square root of 5 times 5?

• -5

• -2

• -10

• -25

How do you simplify a perfect square factor?

• Multiply the radicands

• Take the square root

• Divide the coefficients

• Add the coefficients

What is the final simplified result of the second example?

• -4 - 5 square roots of 10

• -5 - 4 square roots of 10

• -5 + 4 square roots of 10

• -4 + 5 square roots of 10