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

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.

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

E. F.G.

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:

***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.

C.D. E.F.

G.H. I.J.

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.

C.D.

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

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