Basic Mathematics for College Students

Chapter 4 Summary and Review 407

When evaluating an expression containing square
roots,evaluate square roots at the same stage in
your solution as exponential expressions.

Evaluate:

Perform the operations within the parentheses first.

Within the parentheses,

evaluate the exponential

expression and the square

root.

Within the parentheses, do

the multiplication.

Within the parentheses, do

the subtraction.

Do the multiplication.

 4 Do the addition.

 20 (24)

 20 6(4)

 20 6(812)

20  6123  4192  20 6( 8  4  3 )

20  6123  4192

To evaluate formulas that involve square roots,we
replace the letters with specific numbers and then
use the order of operations rule.

Evaluate for and.

This is the formula to evaluate.

Replace cwith 25 and bwith 20.

Evaluate the exponential expressions.

Do the subtraction.

 15 Evaluate the square root.

 1225

 1625  400

 2252  202

a 2 c^2 b^2

a 2 c^2 b^2 c 25 b 20

If a number is not a perfect square, we can use the
square root key on a calculator (or a table of
square roots) to find its approximate square root.

1

Approximate. Round to the nearest hundredth.

From a scientific calculator we get. Rounded

to the nearest hundredth,

1149 12.21

1149 12.20655562

1149

109. Find the two square roots of 25.


110. Fill in the blanks: because.

Evaluate each square root without using a calculator.

111. 
     
     
     
     112. 
          
     
     
     
     


112. 
     
     
     
     114. 
          
     
     
     
     


113. 
     
     
     
     116. 
          
     
     
     
     


114. 
     
     
     
     118. 
          
     
     
     
     


115. Graph each square root: , , ,
     (Hint:Use a calculator or square root table to
     approximate any square roots, when necessary.)


116. Use a calculator to approximate each square root
     to the nearest hundredth.
     a. 119 b. 1598 c. 1 12.75

− 5 − 4 − 3 − 2 −10 12 34 5

19  1213  116

 10

B

1

36

1 0.81

B

64

169

1100 1 0.09

149  116

149 ^2  49

Evaluate each expression without using a calculator.

125.

126.

127. Evaluate for and.


128. SHEET METAL Find the length of the side of the
     range hood shown in the illustration below.


129. Between what two whole numbers would be
     located when graphed on a number line?


130. .Explain why an symbol is used and
     not an symbol.

17  2.646 

183

1,089 in.

b 2 c^2 a^2 c 17 a 15

1 7[6^2 (12) 181 D

40 6[5^2 (72) 116 D

B

100

9

 3149  136  1225

 31100 51196

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