Hawkes Learning Systems: College Algebra

1. Hawkes Learning Systems: College Algebra Section 1.4b: Properties of Radicals

2. Objectives • Combining radical expressions. • Rational number exponents.

3. Combining Radical Expressions Often, a sum of two or more radical expressions can be combined into one. This can be done if the radical expressions are like radicals, meaning that they have the same index and the same radicand. It is frequently necessary to simplify the radical expressions before it can be determined if they are like or not.

4. Like and Unlike Radicals Like Unlike The expression below cannot be combined because the radicand is not the same, therefore making this radical expression an unlike radical. The expression below can be combined because both the index and radicand are the same, therefore making the radical expressions like radicals. Likewise, the below expression also cannot be combined because the index is not the same, therefore making this radical expression an unlike radical.

5. Example: Combine Radical Expressions Combine the Radical Expressions, if possible. a) b)

6. Rational Number Exponents Meaning of : If n is a natural number and if is a real number, then and

7. Rational Number Exponents Meaning of : If m and n are natural numbers, then Either can be used to evaluate as they are equal. Note: is defined to be

8. Example: Rational Number Exponents Simplify. a) b) c)

9. Simplify Radicals Simplify. a) b)