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

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

3. 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

4. Combining Like Radicals
Radical Expressions
Combining Like Radicals
Solution

5. Combining Like Radicals
Radical Expressions
Combining Like Radicals
Solution Continued
Solution

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

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

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

9. Multiplying Radical Expressions
Finding Products of Radical Expressions
Solution Continued
Example

10. 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

11. 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:

12. Multiplying Radical Expressions
Simplifying Radical Expressions
Solution Continued
Solution
Simplify
Example

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

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

15. Multiplying Radical Expressions
Example
Find the product.
Solution

16. Multiplying Radical Expressions
Solution Continued
Example
Find the product.

17. 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:

18. 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.

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

20. 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.

21. 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.