5.5 ROOTS AND REAL NUMBERS5.6 RADICAL EXPRESSIONSAlgebra 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.

#n

2a b

,na b

I. Simplify.

A. B.

C. D.

4169x 3 6125a

3 343 4211y

E. F. G.48169 yx 3 65g 25

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:

nnn baab

n

nn

b

a

b

a

***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.

4 925a b 3300a

C. D.

E. F.

4 5 754x y z 3 6 2125t w

3 2 37 27 4 8n n 2 310 40x y xy

G. H.

I. J.

8

7

y

x32

9x

20 8

2 2

6

2 3

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.

3 2; 2

4 43 2 ;4 2x x

2 20 2 45 3 80 2 3 5 7 3 2

C. D.3 27 7 3 12 6 6 3 24 150

III. Multiplying Radicals by using the FOIL METHOD.

** Multiply the coefficients and the radicands.**

A. B.

2 6 3 2 3 2 2 2 3 4 5 3 6 5

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

A. B. 3 2

3 5

2 3

2 7