Rationalizing Numerators and Denominators

This video tutorial focuses on rationalizing the numerator in fractions containing radicals. It begins with a simple example, explaining the concept of using the conjugate to eliminate radicals from the numerator. The tutorial progresses to more complex examples, demonstrating the process step-by-step. Finally, it covers rationalizing both the numerator and denominator, providing a comprehensive understanding of the topic.

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

• Subtract the reciprocal

• Multiply by the conjugate

• Multiply by the reciprocal

• Add the conjugate

In the expression 3 minus the square root of 5 over 4, what is the conjugate of the numerator?

• 3 plus the square root of 5

• 3 minus the square root of 5

• 4 minus the square root of 5

• 4 plus the square root of 5

After multiplying by the conjugate, what is the simplified form of the expression 3 minus the square root of 5 over 4?

• 4 over 3

• 3 over 4

• 1 over 3 plus the square root of 5

• 1 over 3 minus the square root of 5

When rationalizing a more complex expression, what happens to the middle terms after multiplying by the conjugate?

• They double

• They cancel out

• They remain unchanged

• They are squared

In the expression involving the square root of x plus two, what is the result after simplifying the numerator?

• x minus 9

• x plus 9

• x minus 7

• x plus 7

What is the first step in rationalizing both the numerator and the denominator?

• Subtract the numerator from the denominator

• Multiply the denominator by its conjugate

• Add the numerator and denominator

• Multiply the numerator by its conjugate

What is the conjugate of 3 minus the square root of x?

• 3 times the square root of x

• 3 plus the square root of x

• 3 minus the square root of x

• 3 divided by the square root of x

How do you handle expressions like x minus 9 and 9 minus x?

• Add them together

• Divide them

• Factor out a negative one

• Multiply them

What is the final simplified form of the expression after rationalizing both the numerator and the denominator?

• Positive 1

• Negative 1

• Zero

• Undefined

What is the purpose of rationalizing the numerator and denominator in a fraction?

• To change the sign

• To add complexity

• To eliminate radicals

• To make the fraction larger