Multiplying and Rationalizing Expressions

The video tutorial explains how to rationalize the denominator of an expression by using the conjugate. It begins by defining rationalization and the need to eliminate square roots from the denominator. The process involves multiplying both the numerator and denominator by the conjugate of the denominator. The tutorial then details the steps of distributing terms, calculating products, and simplifying the expression to achieve a rationalized denominator. The video concludes with a simplified expression and a brief summary of the process.

What does it mean to rationalize the denominator?

• To remove fractions from the numerator

• To create an equivalent expression without square roots in the denominator

• To add square roots to the numerator

• To simplify the entire expression

What is the conjugate of a binomial with subtraction?

• Multiply by the same binomial

• Change addition to subtraction

• Divide by the same binomial

• Change subtraction to addition

Why do we multiply both the numerator and denominator by the conjugate?

• To eliminate the numerator

• To form an equivalent expression

• To create a different expression

• To change the expression

What is the result of multiplying 7x by 7x?

• 49x

• 7x^2

• 14x

• 49x^2

What happens to the middle terms when multiplying conjugates?

• They add up

• They remain unchanged

• They cancel each other out

• They double

What does the square root of 5 times the square root of 5 simplify to?

• 5

• 1

• 10

• 25

What is the simplified form of 49x^2 times 5?

• 245x

• 49x^2

• 245x^2

• 5x^2

What is the final simplified expression in the denominator?

• 245x^2 - 12y^2

• 49x^2 + 12y^2

• 49x^2 - 12y^2

• 245x^2 + 12y^2

What is the purpose of rationalizing the denominator?

• To make the expression more complex

• To simplify the expression

• To add square roots to the numerator

• To eliminate square roots from the denominator

What is the result of multiplying negative two y square root three by two y square root three?

• 4y^2

• -4y^2

• -4y^2 times 3

• 4y^2 times 3