Rationalizing Denominators and Conjugates

The video tutorial explains how to rationalize the denominator of a radical expression by eliminating the radical. It introduces the concept of using the conjugate of the denominator to achieve this. Two examples are provided: the first involves a denominator with a sum involving a square root, and the second involves a difference. The tutorial walks through the multiplication process, simplifying the expression, and ensuring the denominator is rationalized. The video concludes with a summary of the steps and the importance of rationalizing denominators.

What is the primary goal when rationalizing the denominator of a radical expression?

• To add more radicals to the expression

• To eliminate the radical from the denominator

• To make the numerator a perfect square

• To change the sign of the numerator

When the denominator contains a sum or difference involving a square root, what should you multiply by?

• The same expression

• The square of the expression

• The conjugate of the denominator

• The reciprocal of the expression

In the first example, what is the conjugate of the denominator 3 + sqrt(7)?

• 3 - sqrt(7)

• sqrt(7) - 3

• 7 - sqrt(3)

• 3 + sqrt(7)

After multiplying by the conjugate in the first example, what is the simplified denominator?

• 9

• 0

• 7

• 2

What common factor is factored out from the numerator in the first example?

• 1

• 3

• 7

• 2

What is the final simplified form of the expression in the first example?

• -3 + sqrt(7)

• 7 - sqrt(3)

• sqrt(7) - 3

• 3 - sqrt(7)

In the second example, what is the conjugate of the denominator 9 - sqrt(3)?

• 9 + sqrt(3)

• 9 - sqrt(3)

• sqrt(3) - 9

• 3 + sqrt(9)

What is the result of simplifying the denominator in the second example?

• 0

• 3

• 78

• 81

Why do the middle terms in the product of the conjugate and the original expression cancel out?

• They are opposites

• They are both zero

• They are both perfect squares

• They are identical

What is the main benefit of rationalizing the denominator?

• It changes the sign of the expression

• It increases the value of the expression

• It eliminates radicals from the denominator

• It makes the expression more complex