RATIONALIZE THE DENOMINATOR

Front

What does it mean to rationalize the denominator?

Back

To rationalize the denominator means to eliminate any radical (square root) expressions from the denominator of a fraction.

Front

Why is it important to rationalize the denominator?

Back

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

Front

What is the general method for rationalizing a denominator that contains a square root?

Back

Multiply the numerator and the denominator by the radical in the denominator.

Front

Rationalize the denominator: (1/√2)

Back

(√2/2) - Multiply by √2/√2.

Front

Rationalize the denominator: (3/√5)

Back

(3√5/5) - Multiply by √5/√5.

Front

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

Back

(2√3/3) - Multiply by √3/√3.

Front

How do you rationalize a denominator with a binomial?

Back

Multiply the numerator and denominator by the conjugate of the denominator.

Front

What is the conjugate of (a + b)?

Back

The conjugate is (a - b).

Front

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

Back

(2 - √3)/(4 - 3) = 2 - √3.

Front

What is the result of rationalizing (5/(1 - √2))?

Back

(5(1 + √2))/(1 - 2) = -5(1 + √2).