Rationalizing the Denominator

Front

What does it mean to rationalize the denominator?

Back

To rationalize 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 the numerator and 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 (2-√3)/(2-√3) to get (3(2-√3))/(4-3) = 3(2-√3)/1 = 6-3√3.

Front

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

Back

(5/√5) * (√5/√5) = 5√5/5 = √5.

Front

What happens when you rationalize a denominator with a binomial?

Back

You multiply by the conjugate of the binomial to eliminate the square root.

Front

Rationalize the denominator: 4/(√2 + 1)

Back

Multiply by (√2 - 1)/(√2 - 1) to get (4(√2 - 1))/(2 - 1) = 4(√2 - 1).

Front

What is the conjugate of a binomial expression a + b?

Back

The conjugate is a - b.

Front

Rationalize the denominator: 1/(3 - √2)

Back

Multiply by (3 + √2)/(3 + √2) to get (3 + √2)/(9 - 2) = (3 + √2)/7.