Algebra and General Mathematics: Rationalization

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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