Intermediate Algebra (11th edition)

OBJECTIVE 5 Use a calculator to find roots. While numbers such as and

are rational, radicals are often irrational numbers. To find approximations of

such radicals, we usually use a scientific or graphing calculator. For example,

and

where the symbol means “is approximately equal to.” In this book, we often show

approximations rounded to three decimal places. Thus,

and

FIGURE 5shows how the preceding approximations are

displayed on a TI-83/84 Plus graphing calculator.

There is a simple way to check that a calculator

approximation is “in the ballpark.” For example, because

16 is a little larger than 15, should be a little

larger than Thus, 3.873 is reasonable as an ap-

proximation for 215.

215.

216 = 4

215 L3.873, 2310 L2.154, 242 L1.189.

L

215 L3.872983346, 2310 L2.15443469, 242 L1.189207115,

23 - 8

29

432 CHAPTER 8 Roots, Radicals, and Root Functions

FIGURE 5

NOTE The methods for finding approximations differ among makes and models of

calculators. You should always consult your owner’s manual for keystroke instruc-

tions.Be aware that graphing calculators often differ from scientific calculators in

the order in which keystrokes are made.

Finding Approximations for Roots

Use a calculator to verify that each approximation is correct.

(a) (b)

(c) 2393 L4.531 (d) 2439 L2.499 NOW TRY

239 L6.245 - 272 L-8.485

EXAMPLE 6

Using Roots to Calculate Resonant Frequency

In electronics, the resonant frequency ƒ of a circuit may be found by the formula

where ƒ is in cycles per second, Lis in henrys, and Cis in farads. (Henrys and farads are

units of measure in electronics.) Find the resonant frequency ƒ if

and Give your answer to the nearest thousand.

Find the value of ƒ when and

Given formula

Substitute for Land C.

Use a calculator.

The resonant frequency ƒ is approximately 411,000 cycles per sec. NOW TRY

L411,000

=

1

2 p 215 10 -^4213 10 -^102

ƒ =

1

2 p 2 LC

L= 5 10 -^4 C= 3 10 -^10.

C= 3 * 10 -^10 farad.

L= 5 * 10 -^4 henry

ƒ=

1

2 p 2 LC

,

EXAMPLE 7

NOW TRY
EXERCISE 6
Use a calculator to approxi-
mate each radical to three
decimal places.

(a) (b)

(c) 2533

- 292 2439

NOW TRY
EXERCISE 7
Use the formula in Example 7
to approximate ƒ to the near-
est thousand if

and C= 3 * 10 -^9.

L= 7 * 10 -^5

NOW TRY ANSWERS

6. (a) (b)2.499
   (c)2.012


7. 347,000 cycles per sec
   
   
   • 9.592