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 can simplify expressions and make them easier to work with, especially in further calculations.

Front

Simplify: 1/√2

Back

√2/2

Front

Simplify: 3/√5

Back

3√5/5

Front

What is the result of multiplying the numerator and denominator by the same radical?

Back

It does not change the value of the fraction, but it can simplify the expression.

Front

Simplify: 4/√3

Back

4√3/3

Front

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

Back

The conjugate is a - b.

Front

Simplify: (2 + √3)/(1 - √3)

Back

(2 + √3)(1 + √3)/(1 - 3) = (2 + 2√3 + 3)/(−2) = (5 + 2√3)/(-2) = -5/2 - √3.

Front

What is the formula for rationalizing a denominator with a binomial?

Back

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

Front

Simplify: 5/(2 + √3)

Back

5(2 - √3)/(4 - 3) = 5(2 - √3) = 10 - 5√3.