Rationalizing Denominators Multiplying Radicals Conjugates Simplifying Expressions with Radicals in the denominator a) Eg.1 Simplify (32-23)(52)(-33) To multiply monomials you may first with to write the radicals in simplest form. Compare these two procedures. (38)(212)=3(22)||2(23)] (38)(212)=696 Recall: Eg.2 (a+b)(c+d)= ac+ad+bc+bd and 55=5 Simplify (25-3)(35+2) b) You should not have a radical in the denominator of a rational expression, so we must get rid of the radical by rationalizing the denominator. In order to rationalize the denominator you multiply by the conjugate of the radical. Eg.4 Simplify the following; 33-22 a) 3-2 ; since there is a radical on the bottom, we must rationalize the denominator by multiplying by the conjugate. 23-32 b) 52 ; Recall that (a-b)(a+b)=a-b