Basic Mathematics for College Students

406 Chapter 4 Decimals

107. ROADSIDE EMERGENCY What is the area of
     the reflector shown below?


108. SEAFOOD A shopper purchased pound of crab^34

10.9 in.

6.4 in.

100. Graph 1.125, , , and on a number line.

Evaluate each expression. Work in terms of fractions.

101. 
     
     
     
     102. 
          
     
     
     
     

Evaluate each expression. Work in terms of decimals.

103. 
     
     
     
     104. 
          
     
     
     
     


104. 
     
     
     
     106. 7.5(0.78)a
     
     
     
     

1

2

b

1 2

2

(9.78.9)(10)

1

8

a7.3 5

9

10

b

4

5

(7.8)

5

6

0.19

1

3

0.4

− 5 − 4 − 3 − 2 −10 12 34 5

3.3 2 34  109

meat, priced at $13.80 per pound, and pound of

lobster meat, selling for $35.70 per pound. Find the

total cost of these items.

1

3

SECTION 4.6 Square Roots

The square rootof a given number is a number

whose square is the given number.

Every positive number has two square roots. The

number 0 has only one square root.

DEFINITIONS AND CONCEPTS EXAMPLES

Find the two square roots of 81.

9 is a square root of 81 because

and

 9 is a square root of 81 because (9)^2  81.

92  81

A radical symbol is used to indicate a positive

square root. To evaluate a radical expressionsuch

as , find the positive square root of the

radicand.

Radical symbol

Radicand Read as “the

square root of 4.”

14 

14

1 Evaluate each square root:

Ask: What positive number, when squared, is 4?

The answer is 2 because 2^2 = 4.

Ask: What positive number, when squared, is 64?

The answer is 8 because 8^2 64.

Ask: What positive number, when squared, is 225?

The answer is 15 because 15^2 225.

1225  15

164  8

14  2

Radical expression

Numbers such as 4, 64, and 225, that are squares of

whole numbers, are called perfect squares. To

evaluate square root radical expressions, it is helpful

to be able to identify perfect square radicands.

Review the list of perfect squares on page 00.

b

The symbol is used to indicate the negative

square rootof a positive number. It is the opposite

of the positive square root.

 1 Evaluate:

is the opposite (or negative) of the square root of 36. Since

, we have:

 136  6

136  6

 136

 136

We can find the square root of fractions and

decimals.

Evaluate each square root:

Ask: What positive fraction, when squared, is?

The answer is because.

Ask: What positive decimal, when squared, is 0.25?

The answer is 0.5 because (0.5)^2 0.25.

1 0.25

107 110722  10049

49

B^100

49

100