Rationalizing the denominator with a radical in the numerator and denominator

The video tutorial explains how to simplify a radical expression by rationalizing the denominator, especially when dealing with binomials. It introduces the concept of using a conjugate to eliminate radicals and demonstrates the multiplication of binomials. The tutorial highlights common mistakes, such as forgetting parentheses, and guides through the simplification process to reach the final expression.

What is the purpose of using a conjugate when rationalizing the denominator?

• To simplify the numerator

• To eliminate the radical in the denominator

• To add complexity to the expression

• To change the numerator

When multiplying binomials, what happens to the middle terms?

• They become radicals

• They cancel out

• They remain unchanged

• They double

What is the result of multiplying sqrt(3) by sqrt(3)?

• sqrt(9)

• 3

• sqrt(6)

• 6

How do you combine like terms with radicals?

• By dividing the coefficients

• By multiplying the coefficients

• By subtracting the coefficients

• By adding the coefficients

What is the final simplified form of the expression in the video?

• 10 + 5 sqrt 3

• 12 + 6 sqrt 3

• 13 + 7 sqrt 3

• 15 + 9 sqrt 3