Intermediate Algebra (11th edition)

If nis even, the two nth roots of aare often written together as with

read “positive or negative,” or “plus or minus.”

 

n

2 a,

SECTION 8.1 Radical Expressions and Graphs 429

NOW TRY
EXERCISE 2
Find each root.

(a) (b)

(c) 25 - 32 (d) - 2364

- 225 24 - 625

Finding Roots

Find each root.

(a)

Because the radicand, 100, is positive,there are two square roots: 10 and.

We want the principal square root, which is 10.

(b)

Here, we want the negative square root,.

(c) Principal 4th root (d) Negative 4th root

Parts (a) – (d) illustrate Case 1 in the preceding box.

(e)

The index is evenand the radicand is negative,so is not a real number.

This is Case 2 in the preceding box.

(f ) because (g) because

Parts (f ) and (g) illustrate Case 3 in the box. The index is odd,so each radical

represents exactly one nth root (regardless of whether the radicand is positive, neg-

ative, or 0).

238 =2, 23 =8. 23 - 8 =-2, 1 - 223 =-8.

24 - 81

24 - 81

2481 = 3 - 2481 = - 3

- 10

- 2100 = - 10

- 10

2100 = 10

EXAMPLE 2

OBJECTIVE 3 Graph functions defined by radical expressions.A radical

expressionis an algebraic expression that contains radicals.

and Examples of radical expressions

In earlier chapters, we graphed functions defined by polynomial and rational

expressions. Now we examine the graphs of functions defined by the basic radical

expressions and

FIGURE 1shows the graph of the square root function,together with a table of

selected points. Only nonnegative values can be used for x, so the domain is

Because is the principal square root of x, it always has a nonnegative value, so

the range is also 3 0, q 2.

2 x

3 0, q 2.

ƒ 1 x 2 = 2 x ƒ 1 x 2 = 23 x.

3 - 2 x, 23 x, 22 x- 1

0

2

1

3

x

y

194

0

1

2

3

0

1

4

9

x f f (x) x

f (x) x

FIGURE 1

Square root function

Domain:

Range: 3 0, q 2

3 0, q 2

ƒ 1 x 2  2 x

NOW TRY ANSWERS

2. (a)
   (b)It is not a real number.
   (c) - 2 (d) - 4
   
   
   • 5
   
   
   
   

NOW TRY