HFCC Math Lab Intermediate Algebra  17 DIVIDING RADICALS AND RATIONALIZING THE DENOMINATOR


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1 HFCC Math Lab Intermediate Algebra  17 DIVIDING RADICALS AND RATIONALIZING THE DENOMINATOR Dividing Radicals: To divide radical expression we use Step 1: Simplify each radical Step 2: Apply the Quotient rule for Radicals Rule1: & Rule2: Step 3: After applying the rule simplify the expression if possible. Ex 1: Simplify Applying Rule 1: Simplify the expression inside the radicals: Ex 2: Simplify Applying Rule 2: Simplify the expression inside the radical: Revised 04/10 1
2 Ex 3: Simplify Simplifying: Applying Rule 1: Simplify the expression inside the radicals Ex 4: Simplify Simplifying the expression inside the radicals Applying Rule 2: Simplify the expression inside the radical Exercises: Divide and simplify using the following radical expressions Revised 04/10 2
3 Rationalizing the Denominator: In order for a radical expression to be in the simplest radical form, there can be no fractions under the radical sign and no radicals in the denominator of the fraction. The process of removing the radicals from the denominator is called rationalizing the denominator. A. Rationalizing the denominator when the denominator has only one term with index n Step 1: Simplify any radicals in the numerator and the denominator. Step 2: Determine the factor needed to make the denominator radicand a perfect n th power Step 3: Multiply the numerator and denominator with the factor determined in step 2 Step 4: Simplify the resulting expression if possible Ex 5: Rationalize the denominator Step 1: Simplify the radical Step 2: The factor required to make the denominator radicand a perfect 2 nd power is Step 3: Multiplying the numerator and denominator by : Step 4: Simplify the resulting expression: Ex 6: Rationalize the denominator Step 1: Simplify the radical Step 2: The factor required to make the denominator radicand a perfect 3 rd power is Step 3: Multiplying the numerator and denominator by : Revised 04/10 3
4 Step 4: Simplify the resulting expression: Ex 7: Rationalize the denominator Step 1: Simplify the radical Step 2: The factor required to make the denominator radicand a perfect 3 rd power is Step 3: Multiplying the numerator and denominator by : Step 4: Simplify the resulting expression: Ex 8: Rationalize the denominator Step 1: Simplify the radical Step 2: The factor required to make the denominator radicand a perfect 3 rd power is Step 3: Multiplying the numerator and denominator by : Step 4: Simplify the resulting expression: Revised 04/10 4
5 B. Rationalizing the denominator with two terms, one or both of which involve square root. Recall that the binomials and are called the conjugates. And the difference of square formula the product of the conjugates will result in. Step 1: Multiply the numerator and denominator by the conjugate of the denominator Step 2: Simplify the resulting expression if possible Ex 9: Rationalize the denominator Step1: Multiplying the numerator and denominator with the conjugate of the denominator: Step 2: Simplify: Ex 10: Rationalize the denominator Step1: Multiplying the numerator and denominator with the conjugate of the denominator: Step 2: Simplify: Ex 11: Rationalize the denominator Step1: Multiplying the numerator and denominator with the conjugate of the denominator: Step 2: Simplify: Revised 04/10 5
6 Exercises: Rationalize the denominator in each of the following. Assume that the variable are positive and the denominator is equal to zero Solutions to the Exercise problems: Exercises: Divide and simplify using the following radical expressions Revised 04/10 6
7 Revised 04/10 7
8 Revised 04/10 8
9 You can get additional instruction and practice by going to the following website This website provides good review and practice problems for quotient rule and rationalizing the denominator _addrad.htm This website provides good review and practice for rationalizing the denominator This website provides good review and practice for rationalizing the denominator Revised 04/10 9
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