Rationalizing Denominators in Algebra

The video tutorial explains how to rationalize denominators in fractions, focusing on converting irrational denominators into rational ones. It begins with a simple example using the square root of 2, then progresses to more complex cases involving binomials and variables. The tutorial highlights the importance of rationalizing for consistency, ease of computation, and aesthetics. Techniques such as multiplying by the conjugate and using the difference of squares are demonstrated.

Why is it sometimes necessary to rationalize the denominator?

• To make the numerator a whole number

• To ensure the denominator is a rational number

• To make the fraction easier to read

• To convert the fraction into a decimal

What is the first step in rationalizing the denominator of 1 over the square root of 2?

• Multiply the numerator and denominator by 2

• Subtract 2 from both the numerator and denominator

• Multiply the numerator and denominator by the square root of 2

• Add 2 to both the numerator and denominator

After rationalizing the denominator of 1 over the square root of 2, what is the new denominator?

• 1

• Square root of 2

• Square root of 4

• 2

What is the simplified form of 7 over the square root of 15 after rationalizing the denominator?

• 7 times the square root of 15 over 3

• 7 times the square root of 15 over 7

• 7 times the square root of 15 over 5

• 7 times the square root of 15 over 15

Why can't you simply multiply by the square root of 5 over the square root of 5 to rationalize the denominator of 12 over 2 minus the square root of 5?

• It will make the numerator irrational

• It will not eliminate the irrational number in the denominator

• It will make the fraction undefined

• It will make the denominator zero

What technique is used to rationalize the denominator of a binomial like 2 minus the square root of 5?

• Subtracting the same number from both numerator and denominator

• Adding the same number to both numerator and denominator

• Dividing by the square root of the binomial

• Multiplying by the conjugate

What is the result of multiplying 2 minus the square root of 5 by its conjugate?

• 5

• Negative 1

• 0

• 1

In the example 5y over 2 times the square root of y minus 5, what is the first step to rationalize the denominator?

• Subtract 5 from both the numerator and denominator

• Multiply by the conjugate

• Add 5 to both the numerator and denominator

• Multiply by 2

What is the simplified form of the denominator after rationalizing 5y over 2 times the square root of y minus 5?

• 4y minus 25

• 4y plus 25

• 2y minus 5

• 2y plus 5

What is the simplified form of the numerator after rationalizing 5y over 2 times the square root of y minus 5?

• 5y square roots of y minus 25y

• 10y square roots of y plus 25y

• 10y square roots of y minus 25y

• 5y square roots of y plus 25y