Rationalizing Denominators

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 conjugate of a binomial expression a + b?

Back

The conjugate of a + b is a - b.

Front

How do you rationalize a denominator that is a single square root?

Back

Multiply the numerator and denominator by the square root to eliminate the square root from the denominator.

Front

Rationalize the denominator: 1/√2

Back

Multiply by √2/√2 to get √2/2.

Front

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

Back

Multiply by the conjugate (2 - √3)/(2 - √3) to get (3(2 - √3))/(4 - 3) = 3(2 - √3).

Front

What is the result of rationalizing the denominator of 5/(√5 + 1)?

Back

Multiply by the conjugate (√5 - 1)/(√5 - 1) to get (5(√5 - 1))/(5 - 1) = (5√5 - 5)/4.

Front

What happens when you multiply a binomial by its conjugate?

Back

You get the difference of squares: (a + b)(a - b) = a² - b².

Front

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

Back

Multiply by the conjugate (√7 + 2)/(√7 + 2) to get (4(√7 + 2))/(7 - 4) = (4√7 + 8)/3.

Front

What is the first step in rationalizing a denominator with a binomial?

Back

Identify the conjugate of the binomial and multiply both the numerator and denominator by it.