Simplifying a radical expression by rationalizing the denominator as a binomial

The video tutorial demonstrates how to simplify a radical rational expression by rationalizing the denominator. It explains the necessity of using the conjugate when the denominator is a binomial, leading to the difference of two squares. The process involves multiplying the numerator and denominator by the conjugate, simplifying the expression, and arriving at the final answer. The tutorial concludes with a summary of the steps taken to achieve the simplified expression.

Why can't we simply multiply by the square root of 10 on both the numerator and denominator when rationalizing a binomial denominator?

• It would result in a zero denominator.

• It would make the expression more complex.

• It would not eliminate the radical.

• It would not change the expression.

What is the purpose of multiplying a binomial by its conjugate?

• To add more terms to the expression.

• To create a sum of squares.

• To eliminate the numerator.

• To produce a difference of two squares.

What is the result of multiplying a binomial by its conjugate?

• A product of two binomials.

• A difference of two squares.

• A sum of cubes.

• A single term.

What is the simplified form of the numerator in the expression?

• 21 + 7 sqrt 10

• 21 - 7 sqrt 10

• 7 + 21 sqrt 10

• 7 - 21 sqrt 10

What is the final simplified form of the expression after distributing the negative sign?

• -21 - 7 sqrt 2

• -21 - 7 sqrt 10

• -21 + 7 sqrt 2

• -21 + 7 sqrt 10