Algebra and General Mathematics: Rationalization

Review notes in Rationalization topic in Algebra and General Mathematics. This will help you prepare in taking the Engineering Board Exam or simply reviewing for your Algebra subject.

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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