(Last Updated On: February 5, 2020)

#### RATIONALIZATION

To rationalize the denominator of a fraction means to remove all radicals from the denominator.

**To rationalize a denominator, multiply both the numerator and denominator by an appropriate factor that will make the denominator free from radicals.**

**Example:**

**Rationalizing Single-Term Denominator**

**Rationalize the fraction, 4 / 5√2**

**= [ 4 / (5√2) ] [ √2 / √2 ]**

**= 4√2 / 10**

**= 2√2 / 5**

**Example:**

**Rationalizing Two-Term Denominator**

**Rationalize the fraction, 3 / (2 + √5)**

**= 3 / (2 + √5) [ (2 – √5) / 2 – √5) ] → multiply by conjugate**

**= [ 3(2 – √5) ] / [ (22 – √52) ]**

**= -3(2 – √5)**

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