Rationalizing Denominators and Expressions

The video tutorial explains how to rationalize the denominators of fractions. It begins with an introduction to the concept, followed by two examples. The first example involves rationalizing a fraction with the square root of 45 in the denominator, using prime factorization to simplify. The second example demonstrates rationalizing a fraction with the square root of x cubed in the denominator, highlighting the need for perfect square factors. The tutorial concludes with a summary of the rationalization process.

What is the first step in rationalizing the denominator of a fraction?

• Add a radical to the numerator

• Multiply the numerator and denominator by the same radical

• Divide the numerator by the denominator

• Subtract a radical from the denominator

Why is the square root of 45 considered irrational?

• It is a perfect square

• It is a prime number

• It is an even number

• It cannot be simplified perfectly

What is the perfect square factor of 45?

• 5

• 9

• 15

• 3

What do you multiply by to rationalize the denominator in the first example?

• Square root of 15

• Square root of 9

• Square root of 3

• Square root of 5

What is the result of rationalizing the denominator in the first example?

• Square root of 5y over 5

• Square root of 5y over 15

• Square root of 5y over 9

• Square root of 5y over 3

In the second example, what is the initial expression given?

• Square root of x cubed over 2

• Square root of x over 2

• Square root of 2 over x cubed

• Square root of 2 over x squared

What is the perfect square factor in the denominator of the second example?

• x to the fourth

• x cubed

• x

• x squared

What do you multiply by to rationalize the denominator in the second example?

• Square root of 2

• Square root of x

• Square root of x squared

• Square root of x cubed

What is the final expression after rationalizing the denominator in the second example?

• Square root of 2x over x

• Square root of 2x over 2x

• Square root of 2x over x squared

• Square root of 2x over x cubed

What is the purpose of rationalizing the denominator?

• To add more radicals to the expression

• To simplify the numerator

• To eliminate radicals from the denominator

• To make the numerator a perfect square