Understanding Radical Conjugates

The video tutorial explains the concept of radical conjugates, which are two radical expressions that differ only by a sign. It demonstrates how to multiply these conjugates through two examples, showing that the middle terms cancel out, resulting in a simplified product without square roots. The tutorial emphasizes the special nature of this product and provides a detailed walkthrough of each step involved in the multiplication process.

What is a radical conjugate?

• Two expressions with the same terms and operations

• Two expressions with different terms but the same operations

• Two expressions with different terms and operations

• Two expressions with the same terms but different operations

In the first example, what is the result of multiplying the square root of 11 by itself?

• Square root of 121

• 11

• 22

• Square root of 22

Why do the middle terms cancel out in the product of radical conjugates?

• They are both negative

• They are both positive

• They are opposites

• They are identical

What is the significance of the middle terms in the product of radical conjugates?

• They add up to a positive number

• They cancel each other out

• They add up to a negative number

• They remain unchanged

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CCSS.7.NS.A.1C

In the first example, what is the final result after simplification?

• -5

• -11

• 5

• 0

What is the first step in multiplying the second set of radical conjugates?

• Divide the coefficients

• Multiply the coefficients

• Subtract the terms

• Add the terms

In the second example, what is the result of multiplying 7 square root 3 by itself?

• 21

• 49

• 49 square root 3

• 21 square root 3

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CCSS.6.EE.A.1

What is the simplified result of the second example?

• 127

• 147

• 120

• 130

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CCSS.HSN.RN.A.2

What happens to the square roots in the final product of radical conjugates?

• They remain in the expression

• They become negative

• They simplify and disappear

• They double

What is the purpose of multiplying radical conjugates?

• To find the sum of the radicals

• To create a new radical expression

• To increase the complexity of the expression

• To simplify the expression by removing square roots