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# Rationalize Denominators

 Rationalize Denominators MATH 018 Combined Algebra S. Rook

 Overview • Section 10.5 in the textbook: – Rationalizing a denominator with one term – Rationalizing a denominator with two terms

 Rationalizing Denominators with One Term

 Rationalizing Denominators with One Term • Rationalizing: the process of eliminating the radical from either the numerator or denominator of a fraction – We will only be rationalizing the denominator Consider – what happens when we multiply by itself?

 • Thus, we can say: • To rationalize a denominator with one term: – Determine what needs to be multiplied to eliminate the radical in the denominator – Multiply this term times BOTH the numerator and denominator (dealing with an expression) • This eliminates the radical in the denominator – Acceptable to have radicals present in the numerator

 Simplify Radicals Before Rationalizing • Consider rationalizing – Could multiply numerator and denominator by – Easier, however to simplify • Multiply numerator and denominator by instead of • See if radicals can be simplified before rationalizing – Otherwise radicals must be simplified at the end where the numbers are larger

 Rationalizing Denominators with One Term (Example) Ex 1: Rationalize the denominator: Rationalizing Denominators with Two Terms

 Rationalizing Denominators with Two Terms • Again, goal is to eliminate the radicals from the denominator – Consider – Consider • Conjugate: same 2 terms but different signs – Given , what would be its conjugate? • To rationalize a denominator with two terms: – Multiply BOTH the numerator and denominator by the conjugate (dealing with an expression) • Eliminates the radical(s) in the denominator – Acceptable to have radicals present in the numerator • Look to simplify radicals before rationalizing

 Ex 2: Rationalize the denominator: Summary • After studying these slides, you should know how to do the following: – Rationalize denominators containing one or two terms • Additional Practice – See the list of suggested problems for 10.5 • Next lesson – Solving Radical Equations (Section 10.6)