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c) 2 3 ( 6  3 ) 3 d) 2( 2  3 )( 3  ) 1

e) 2( 3  3 )( 3  ) 1 g) ( 2  1 )( 2  ) 1

h) 2( 3  2 )( 2 3  ) 2 i) 5  2  5  2

Binomials Containing Radicals and Conjugates:

Expressions of the form a  b and a  b are called conjugates of each other.

If a and b are integers, the product of the conjugates will be an integer. Conjugates can

be used to rationalize the denominator containing a binomial radical expression.


Remark C: Let a, b  R .

a) The conjugate of a is a .
b) The conjugate of a  b is a  b .
c) The conjugate of a  b is a  b .

Remark D: Multiply the numerator and the denominator of the given fraction

by the conjugate of the denominator to rationalize the denominator of

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