Grade 8
Mathematics
Unit: 06 Lesson: 01
Rational and Irrational Numbers
For problems 1 - 10
• Estimate the square root of each irrational number to the nearest tenth.
• Graph each answer on the number line. Your answer must be on the correct
“half of the half” between the two integers that are boundaries for the square
root.
1.
3 ≈ ________
2.
10 ≈ ________
3.
15 ≈ ________
4.
22 ≈ ________
5.
37 ≈ ________
6.
34 ≈ ________
7.
70 ≈ ________
8.
19 ≈ ________
9.
7 ≈ ________
10.
5 ≈ ________
11. Use a calculator to give the approximate value for 23 to the nearest
hundredth. Write a statement to demonstrate an understanding of the
approximate value of the irrational number.
©2012, TESCCC
04/29/13
page 1 of 4
Grade 8
Mathematics
Unit: 06 Lesson: 01
Rational and Irrational Numbers
Select the best answer. Show all work. Justify your answers.
12. Which statement is TRUE?
A. The
B. The
C. The
D. The
29
33
53
10
is between 4 and 5.
is less than 5.
is between 7 and 8.
is less than 3.
13. Which statement is FALSE?
A. The
B. The
C. The
D. The
78
45
38
13
is between 8 and 9.
is less than 7.
is between 6 and 7.
is less than 3.
14. Mrs. Gebhart decided to replace the carpet with ceramic tile in her home office.
The office is a square with an area of 109 ft 2. What is the length of one side of
the office? (Choose the best estimate.)
A. 10.8 ft
B. 11.2 ft
C. 10.4 ft
D. 9.9 ft
15. After pouring the cement foundation for her new restaurant, Mrs. Gonzalez
decided to paint the floor. The area of the wall was 69 ft 2. What was the length
of one side of the wall? (Choose the best estimate.)
A. 6.9 ft.
B. 8.3 ft.
C. 9.2 ft.
D. 8.8 ft.
©2012, TESCCC
04/29/13
page 2 of 4
Grade 8
Mathematics
Unit: 06 Lesson: 01
Rational and Irrational Numbers
16. Matt wants to build a circular water fountain that has an approximate area of 51
square feet. Matt uses 3 as the approximate value of pi and uses the formula
for the area of a circle, A = π r2, to find that r2 = 17 square feet.
What is the best estimate of the radius of Matt’s circular water fountain?
A.
B.
C.
D.
4.1 feet
3.8 feet
8.5 feet
4.6 feet
17. Mr. Garcia has obtained permission for the JH Art Club to paint a mural on the
square section of the wall by the office. The area of this section of the wall is 68
ft2. What was the length of one side of the wall? (Choose the best estimate.)
A. 7.8 ft
B. 8.3 ft
C. 34 ft
18. Mr. Gaona is going to build a square-shaped storage building in the backyard.
Mr. Gaona uses the formula for the area of a square to determine which of four
given areas would give him a square building with a side length closest to 15
feet. The four areas are 150 ft2, 228 ft2, 300 ft2, and 1150 ft2. Which irrational
number is closest to 15?
A.
150
B.
C.
228
300
D.
1150
©2012, TESCCC
04/29/13
page 3 of 4
Grade 8
Mathematics
Unit: 06 Lesson: 01
Rational and Irrational Numbers
19. Create a concept diagram to compare and contrast the characteristics of Real
Numbers including Rational and Irrational numbers by definition. Give examples
(3 different representations of rational numbers and 2 examples of irrational
numbers). Draw a number line graphing both the rational and irrational
examples described above using appropriate increments.
20. Use a calculator to compare and order the given real numbers.
(A)
(B)
(C)
23 ≈
4.5
1.21
©2012, TESCCC
04/29/13
(D)
(E)
14
=
3
1
0.04
=
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