Adding, Subtracting, and Multiplying Radical Expressions Section 13.2 Adding, Subtracting, and Multiplying Radical Expressions

Combining Like Radicals Radical Expressions Combining Like Radicals Example Combine like radicals Solution

Combining Like Radicals Radical Expressions Combining Like Radicals Solution Continued Example 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 Perform the indicated operations. Example

Combining Like Radicals Radical Expressions Combining Like Radicals Solution

Combining Like Radicals Radical Expressions Combining Like Radicals Solution Continued Solution

Perform the indicated operation. Radical Expressions Adding or Subtracting Radical Expressions Example Perform the indicated operation. Solution

Perform the indicated operation. Radical Expressions Adding or Subtracting Radical Expressions Solution Continued Example Perform the indicated operation.

Multiplying Radical Expressions Finding Products of Radical Expressions Example Find the product. Solution

Multiplying Radical Expressions Finding Products of Radical Expressions Solution Continued Example

Multiplying Radical Expressions Finding Products of Radical Expressions Solution Continued Example If is defined, then In words: The nth power of the nth root of a number is the number. Simplify. Example

Multiplying Radical Expressions Simplifying 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 Continued Solution Simplify . Example

Multiplying Radical Expressions Simplifying the Square of a Radical Expression with Two Terms Solution Another way:

Multiplying Radical Expressions Simplifying the Square of a Radical Expression with Two Terms Warning Simplify Example Solution

Multiplying Radical Expressions Example Find the product. Solution

Multiplying Radical Expressions Solution Continued Example Find the product.

Multiplying Radical Expressions Multiplying Two Radicals with Different Indexes but the Same Radicand 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.

Perform the indicated operations. Assume that x ≥ 0. Multiplying Radical Expressions Simplify Radical Expressions Example Perform the indicated operations. Assume that x ≥ 0. Solution

Perform the indicated operations. Assume that x ≥ 0. 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.