Rationalize the Denominator

Front

What does it mean to rationalize the denominator?

Back

Rationalizing the denominator means to eliminate any irrational numbers (like square roots) from the denominator of a fraction.

Front

Why is it important to rationalize the denominator?

Back

Rationalizing the denominator simplifies expressions and makes them easier to work with, especially in further calculations.

Front

What is the process of rationalizing a denominator that contains a square root?

Back

Multiply both the numerator and the denominator by the square root present in the denominator.

Front

Rationalize the denominator: 1/√2

Back

(1/√2) * (√2/√2) = √2/2.

Front

Rationalize the denominator: 3/(2 + √3)

Back

Multiply by the conjugate: (3/(2 + √3)) * ((2 - √3)/(2 - √3)) = (3(2 - √3))/(4 - 3) = 3(2 - √3).

Front

What is a conjugate in the context of rationalizing denominators?

Back

The conjugate of a binomial expression a + b is a - b. It is used to eliminate the square root when rationalizing.

Front

Rationalize the denominator: 5/(√5 - 1)

Back

Multiply by the conjugate: (5/(√5 - 1)) * ((√5 + 1)/(√5 + 1)) = (5(√5 + 1))/(5 - 1) = (5(√5 + 1))/4.

Front

What happens when you multiply a fraction by 1?

Back

Multiplying by 1 does not change the value of the fraction, as long as the 1 is expressed in a form that is equivalent to 1.

Front

Rationalize the denominator: 4/(√7 + 2)

Back

Multiply by the conjugate: (4/(√7 + 2)) * ((√7 - 2)/(√7 - 2)) = (4(√7 - 2))/(7 - 4) = (4(√7 - 2))/3.

Front

What is the result of rationalizing the denominator of 1/(√3 + √2)?

Back

Multiply by the conjugate: (1/(√3 + √2)) * ((√3 - √2)/(√3 - √2)) = (√3 - √2)/(3 - 2) = √3 - √2.