Beginning Algebra, 11th Edition

Find each square root. See Examples 2 and 4(c).

Find the square of each radical expression. See Example 3.

Concept Check What must be true about the variable a for each statement to be true?

39. represents a positive number. 40. represents a negative number.


40. is not a real number. 42. is not a real number.

Determine whether each number isrational, irrational,ornot a real number.If a number is ra-
tional, give its exact value. If a number is irrational, give a decimal approximation to the
nearest thousandth. Use a calculator as necessary. See Examples 4 and 5.

Concept Check Without using a calculator, determine between which two consecutive inte-
gers each square root lies. For example,

is between 8 and 9 , because and

Work Exercises 63 and 64 without using a calculator.

• 240 - 263 2 23.2 2 10.3

294 243 251 230

275 264 =8, 281 =9, 646756 81.

2 - 29 2 - 47 21200 21500

• 264 - 281 - 2300 - 2500

225 2169 229 233

2 a - 2 a

2 a - 2 a

23 x^2 + 4 29 y^2 + 3

B

5

B 7

2

3

219 259 - 219 - 259

2 - 121 2 - 64 - 2 - 49 - 2 - 100

• 2 0.64 2 0.16
  B

49

36

• B

144

121

• 2196

21 24 249 281 - 2256

SECTION 8.1 Evaluating Roots 501

√103 m

√48 m

√66 ft

√23 ft

63.Choose the best estimate for the length
and width (in meters) of this rectangle.
A.11 by 6 B.11 by 7
C.10 by 7 D.10 by 6

64.Choose the best estimate for the base

and height (in feet) of this triangle.

A. , B. ,

C.b= 9 , h= 5 D.b= 9 , h= 4

b= 8 h= 5 b= 8 h= 4

Find the length of the unknown side of each right triangle with sides a, b, and c, where c is the
hypotenuse. Give any decimal approximations to the nearest thousandth. See FIGURE 1and
Example 6.

65. , 66. , 67. ,

68.a= 5 , c= 13 69.a= 11 , b= 4 70.a= 13 , b= 9

a= 8 b= 15 a= 24 b= 10 a= 6 c= 10