**Definition of Rationalizing the Denominator**

- Rationalizing the denominator is the process by which a fraction containing radicals in the denominator is rewritten to have only rational numbers in the denominator.

**Examples of Rationalizing the Denominator**

In the example above, the radical in the denominator is converted into a rational number by multiplying and dividing the fraction by using the fact that . This process is called â€˜rationalizing the denominator.â€™

Here in the denominator is converted into a rational number by multiplying and dividing the fraction by the conjugate using the fact that .

**Solved Example on Rationalizing the Denominator**

Simplify by rationalizing the denominator.

Choices:

A.

B.

C.

D.

Correct answer: D

Solution:

Step 1:[Use quotient property.]

Step 2:[Use product property.]

Step 3:[]

Step 4:[Multiply by a value of = 1.]

Step 5:

**Related Terms for Rationalizing the Denominator**

- Denominator
- Rational Number
- Fraction