Basic Mathematics for College Students

A portion of the table of square roots from Appendix III on page A-00 is shown
in the margin on the previous page. The table gives decimal approximations of square
roots of whole numbers that are not perfect squares. To find an approximation of
to the nearest thousandth, we locate 17 in the n-column of the table and scan directly
right, to the 1 n-column, to find that 117 4.123.

117

4.6 Square Roots 391

EXAMPLE (^8) Use a calculator to approximate each square root. Round to
the nearest hundredth. a. b. c.
StrategyWe will identify the radicand and find the square root using the
key. Then we will identify the digit in the thousandths column of the display.
WHYTo round to the hundredths column, we must determine whether the digit in
the thousandths column is less than 5, or greater than or equal to 5.
Solution
a.From the calculator, we get. Rounded to the nearest
hundredth,.
b.From the calculator, we get. Rounded to the nearest
hundredth,.
c.From the calculator, we get. Rounded to the nearest
hundredth, 1 0.00450.07.

1 0.00450.067082039

1 56.27.50

1 56.27.496665926

1373 19.31

1373 19.31320792

1

1373 1 56.2 1 0.0045

Self Check 8

Use a calculator to approximate

each square root. Round to the

nearest hundredth.

a.

b.

c.

Now TryProblems 87 and 91

1 0.076

1 607.8

1153

1.8 and  8 2. a. 12 b. 9 3. a. b.0.2 4. a. 12 b. 17 5. a. 88 b. 18

6. 34 7. 8 8. a.12.37 b.24.65 c.0.28

4

7

ANSWERS TO SELF CHECKS

SECTION 4.6 STUDY SET

VOCABULARY

Fill in the blanks.

1. When we raise a number to the second power, we are
   squaring it, or finding its.


2. The square of a given number is a number
   whose square is the given number.


3. The symbol is called a symbol.


4. Label the radicand,the radical expression,and the
   radical symbolin the illustration below.

164 

1

CONCEPTS

Fill in the blanks.

7. a.The square of 5 is , because 5^2 .

b. The square of is , because.

8. Complete the list of perfect squares: 1, 4, , 16, ,
   36, 49, 64, , 100, , 144, , 196,.


9. a. , because^2 49.
   b. , because^2 4.


10. a. , because.

b. , because.

11. Evaluate each square root.
    a. b.


12. Evaluate each square root.
    a. b. c.
    d. 1196 e. 1225

1121 1144 1169

11 10

1 0.16 (0.4)^2 0.16

a

3

4

b

2



9

B 16

9

16



14  2

149  7

a

1

4

b

2



1

4

5. Whole numbers such as 36 and 49, that are squares of
   whole numbers, are called squares.


6. The exact value of is a decimal
   that never repeats.

117

b