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Section 13.2. Adding, Subtracting, and Multiplying Radical Expressions. Example. Combine like radicals. Solution. Radical Expressions. Combining Like Radicals. Example. Solution Continued.
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Section 13.2 Adding, Subtracting, and Multiplying Radical Expressions
Example Combine like radicals Solution Radical Expressions Combining Like Radicals
Example Solution Continued 3. Since the radicals have different indexes, we cannot use the distributive law It’s already simplified 4. Since the radicals have different radicands, we cannot use the distributive law It’s already simplified Perform the indicated operations. Example Radical Expressions Combining Like Radicals
Solution Combining Like Radicals Radical Expressions
Solution Solution Continued Radical Expressions Combining Like Radicals
Example Perform the indicated operation. Solution Radical Expressions Adding or Subtracting Radical Expressions
Example Solution Continued Perform the indicated operation. Radical Expressions Adding or Subtracting Radical Expressions
Example Find the product. Solution Multiplying Radical Expressions Finding Products of Radical Expressions
Example Solution Continued Multiplying Radical Expressions Finding Products of Radical Expressions
Example Solution Continued If is defined, then In words: The nth power of the nth root of a number is the number. Simplify. Example Multiplying Radical Expressions Finding Products of Radical Expressions
Solution 1. Multiply each term of the first factor by each term of the second factor, and combine like radicals: Multiplying Radical Expressions Simplifying Radical Expressions
Solution Solution Continued Simplify . Example Multiplying Radical Expressions Simplifying Radical Expressions
Solution Another way: Multiplying Radical Expressions Simplifying the Square of a Radical Expression with Two Terms
Warning Simplify Example Solution Multiplying Radical Expressions Simplifying the Square of a Radical Expression with Two Terms
Example Find the product. Solution Multiplying Radical Expressions Multiplying Radical Expressions
Example Solution Continued Find the product. Multiplying Radical Expressions Multiplying Radical Expressions
Process To multiply two radicals that have the different index, we use the product property: Multiplying Radical Expressions Multiplying Two Radicals with Different Indexes but the Same Radicand
Process To multiply two radicals with different indexes but the same radicand, 1. Write the radicals in exponential form. 2. Use exponential properties to simplify the expression involving exponents. 3. Write the simplified expression in radical form. Multiplying Radical Expressions Multiplying Two Radicals with Different Indexes but the Same Radicand
Example Perform the indicated operations. Assume that x ≥ 0. Solution Multiplying Radical Expressions Simplify Radical Expressions
Solution Continued Example Perform the indicated operations. Assume that x ≥ 0. Multiplying Radical Expressions Simplify Radical Expressions
Process To simplify a radical expression, 1. Perform any indicated multiplications. 2. Combine like radicals. 3. For any radical with index n, write the radicand as a product of one or more perfect nth powers and another expression that has no factors that are perfect nth powers. Then apply the product property for radicals. 4. Write any radicals with as small an index as possible. Multiplying Radical Expressions Simplify Radical Expressions
