Radical Expressions and Functions10.110.1

1. Find the nth root of a number.2. Approximate roots using a calculator.3. Simplify radical expressions.4. Evaluate radical functions.5. Find the domain of radical functions.

Write as many perfect squares as you can.Write as many perfect squares as you can.

Write as many perfect cubes as you can.Write as many perfect cubes as you can.

Rational expression ↔ fraction

Irrational expression ↔ radical

radicand

root orindex

radical

49 7

25

100 10

36 6

3 8 2

3 27 3

3 125 5

5 32 2

= Not a real number

312564

54

4 4 16

283

• We CANNOT take an even root of a negative number.

The radical symbol represents the positive root.

Evaluating nth roots

• We CAN take an odd root of a negative number.

• If the index is even, there are 2 roots: one positive, one negative.

The positive number is the principle root.

49 Rational expression

732.13

Irrational expression

Exact value

Approximate with calculator

3

Radical function: A function containing a radical expression whose radicand has a variable.

Given f(x) = find f(3). 5 8,x

3 5 3 8f 15 8 7

Graph.

xxf

Domain:

,0

The radicand must be greater than or equal to 0.

Find the domain.

8f x x

8 0x

8x

Domain:

,8

8| xx

Find the domain.

3 9f x x

3 9 0x

3 9x

3x

Domain: 3,

3|

xx

Slide 10- 11Copyright © 2011 Pearson Education, Inc.

Find the domain of f(x) = .

a)

b)

c)

d)

4 16x

4 , or ( , 4]x x

4 , or [4, )x x

4 , or [ 4, )x x

4 , or ( , 4]x x

Slide 10- 12Copyright © 2011 Pearson Education, Inc.

Find the domain of f(x) = .

a)

b)

c)

d)

4 16x

4 , or ( , 4]x x

4 , or [4, )x x

4 , or [ 4, )x x

4 , or ( , 4]x x