1. 5.5 ROOTS AND REAL NUMBERS 5.6 RADICAL EXPRESSIONS Algebra II w/ trig

2. The square root of a number and squaring a number are inverses of each other. indicates the nth root n is the index(if there is not a number there, it is an understood 2), # is the radicand, √ is the radical sign Square Root: if, then a is the square root of b. nth root: if then a is an nth root of b.

3. I. Simplify. A. B. C. D.

4. E. F.G.

5. 5.6 Radical Expressions I. Properties of Square Roots: A. Product Property of Square Roots If a and b are real numbers and n> 1: B. Quotient Property of Square Roots If a and b are real numbers and n> 1:

6. ***You cannot have radicals in the denominator, therefore you have to rationalize the denominator---You must multiply the numerator and denominator by a quantity so that the radicand has an exact root*** II. Simplify Completely A.B.

7. C.D. E.F.

8. G.H. I.J.

9. II. Adding/Subtracting radicals: add only like radicals(same index and same radicand) not like expressions like terms First, simplify roots, then combine like terms. A.B.

10. C.D.

11. III. Multiplying Radicals by using the FOIL METHOD. ** Multiply the coefficients and the radicands.** A.B.

12. IV. Conjugates to rationalize denominator. The conjugate of a-b is a+b, and vice versa. A. B.