Ch 8 - Rational & Radical Functions

1. Ch 8 - Rational & Radical Functions Simplifying Radical Expressions

2. Product Property of Radicals: For any real numbers a and b, then

3. Simplify.

4. Quotient Property of Radicals For any real numbers a and b, and b ≠ 0, if all roots are defined. To rationalize the denominator, you must multiply the numerator and denominator by a quantity so that the radicand has an exact root.

5. Simplify.

6. Two radical expressions are called like radical expressions if the radicands are alike. Conjugates are binomials in the form and where a, b, c, and d are rational numbers. The product of conjugates is always a rational number.

7. Simplify.

8. nth roots • The nth root of a real number a can be written as the radical expression , where n is the index of the radical and a is the radicand.

10. Find all real roots. • Sixth roots of 64 • Cube roots of -216 • Fourth roots of -1024

11. Properties of nth Roots • Product Property of Roots • Quotient Property of Roots

12. Simplify each expression. Assume that all variables are positive.

13. A rational exponent is an exponent that can be expressed as m/n, where m and n are integers and n≠ 0. • The exponent 1/n indicates the nth root. • The exponent m/n indicates the nth root raised to the mth power.

14. Write each expression by using rational exponents. Write each expression in radical form and simplify.

15. Properties of Rational Exponents

16. Simplify each expression.