Easy Algebra Step-by-Step

6 Easy Algebra Step-by-Step

There are infi nitely many other roots—square

roots, cube roots, fourth roots, and so on—that are

irrational. Some examples are 41 ,^3 − 18 , and^4100.

Two famous irrational numbers are π and e. The

number π is the ratio of the circumference of a circle

to its diameter, and the number e is used

extensively in calculus. Most scientifi c

and graphing calculators have π and e

keys. To nine decimal place accuracy,

π ≈ 3.141592654 and e≈ 2. 718281828.

The real numbers, R, are all the

rational and irrational numbers put

together. They are all the numbers on the number line (see Figure 1.7).

Every point on the number line corresponds to a real number, and every real

number corresponds to a point on the number line.

The relationship among the various sets of numbers included in the real

numbers is shown in Figure 1.8.

Problem Categorize the given number according to the various sets of

the real numbers to which it belongs. (State all that apply.)

a. 0

b. 0.

c. –

d. 36

Although, in the past, you might have used 3.

or^22

7

for π, π does not equal either of these

numbers. The numbers 3.14 and^22

7

are rational

numbers, but π is irrational.

Figure 1.7 Real number line

–4 –3 –2 –1 1 2 3 4

–1.

• 
  


• π –0.5 1.4 10
  0

3

5

Figure 1.8 Real numbers

Zero Natural Numbers

Negative Integers Whole Numbers

Nonintegers Integers

Irrational Numbers Rational Numbers

Real Numbers

Be careful: Even roots

(),,^46 , of negative

numbers are not real numbers.