1. Sections 8.1 and 8.2 Radical Expressions Rational Exponents

2. Overview In these sections we expand our understanding of roots beyond square roots. We also introduce rational, or fractional exponents and define them in terms of radical expressions. Finally, we apply already-established properties of exponents to these newly discovered rational exponents.

3. Square Roots A number a is the square root of another number b if For example, 7 is the square root of 49 because It follows that

4. Cube Roots A number c is the cube root of another number d if For example, -4 is the cube root of -64 because It follows that

5. In General… A number y is the nth root of another number z if It follows that

6. More about radicals Given the radical expression n is called the index y is called the radicand If the index is even and the radicand is negative, the radical expression is n.a.r.n. (not a real number)

7. Examples Find each root that is a real number:

8. Rational Exponents A rational exponent is a fractional exponent. Here’s an important definition:

9. More… Another important definition:

10. Examples

11. Finally…. All the rules and properties of exponents discussed in Section 5.1 apply to rational exponents as well as integer exponents. When simplifying these expressions, resist the temptation to change them back to radical form. It usually does not help.

12. Examples