Rationalizing Denominators in Fractions

This video tutorial explains how to rationalize denominators in fractions, focusing on removing radicals from the denominator. It covers various examples, including those with square roots, variables, and cube roots. The tutorial provides step-by-step instructions on multiplying the numerator and denominator by appropriate values to eliminate radicals, ensuring the fraction is simplified. The video also addresses more complex cases involving higher indices and offers practical examples to reinforce the concepts.

What is the primary goal when rationalizing the denominator of a fraction?

• To eliminate the square root from the denominator

• To change the fraction to a decimal

• To add more terms to the numerator

• To make the fraction improper

When rationalizing the denominator of 3/√5, what should you multiply the fraction by?

• 3/3

• 5/5

• 1/1

• √5/√5

In the example of rationalizing 7/√7, what is the result after simplification?

• 1

• 7/49

• 7/√7

• √7/7

How do you handle variables when rationalizing the denominator of a fraction like 7/√x?

• Multiply by 1/1

• Multiply by 7/7

• Multiply by √x/√x

• Multiply by x/x

What is the simplified form of 5/√(x^4 * y^5) after rationalizing the denominator?

• 5y/√(x^2 * y^3)

• 5/√(x^2 * y^3)

• 5y/√(x^4 * y^5)

• 5/√(x^4 * y^5)

When rationalizing the cube root of a denominator, what is the key step?

• Multiply by the cube root of the denominator cubed

• Multiply by the square root

• Multiply by the cube root of the denominator squared

• Multiply by the cube root of the numerator

What is the result of rationalizing 3/∛4?

• 3∛2/2

• 3/∛8

• 3∛4/4

• 3/∛2

In the expression 9/∜(3x), how many 3x terms are needed in the denominator to rationalize it?

• Four

• Three

• Two

• Five

What is the simplified form of 8/∜(32x) after rationalizing the denominator?

• 4∜(2x)/x

• 2/∜(8x^3)

• 2∜(8x^3)/x

• 4/∜(2x)

How do you rationalize a denominator with a seventh root, such as in 6/∜(x^2)?

• Multiply by the seventh root of x^3

• Multiply by the seventh root of x

• Multiply by the seventh root of x^5

• Multiply by the seventh root of x^7