Download Math 8/Unit 07B Practice Test: Roots and The Pythagorean Theorem

Math 8/Unit 07B Practice Test: Roots and The Pythagorean Theorem
Name:
Date:
1. Define perfect square. Give an example of a number that is a perfect square and an
example of a number that is not a perfect square.
2. Define cube root. What is the cube root of 27?
3. Define irrational number and give an example.
4. Use the triangle shown below and label the following: legs, hypotenuse, and right angle.
5. (CRT) List the first 12 perfect squares and their square roots in the table provided.
(CCSS) Then list the first 10 perfect cubes and their cube roots. One of each has been done
for you.
Perfect Square
Square Root
Perfect Cube
Cube Root
4
3
5
216
Math 8 Practice Test
Unit 07B: Roots and The Pythagorean Theorem
Revised 2012 - CCSS
Page 1 of 5
For problems 6 – 9, simplify the expression.
6. 169
7.  81
36
49
8.
9.
3
64
10. (CRT) Look at the numbers below.
7
32 ,  , , 5, 0.7 , 36 , 8
9
What is the order of the numbers from least to greatest?
11.
220 is between what two whole numbers?
A. 219 and 221
B. 110 and 112
C. 14 and 15
D. 13 and 14
12.
45 is not a rational number. Between what two integers does it lie? Which of the two
integers is it closest to and why? Explain your thinking.
13. Determine the value of c in the diagram below. Show your work and label your answer. If
your answer is not rational then state which two integers it is between.
b  5cm
c  ? cm
a  7cm
Math 8 Practice Test
Unit 07B: Roots and The Pythagorean Theorem
Revised 2012 - CCSS
Page 2 of 5
14. Use the diagram below to create a model explaining how the Pythagorean Theorem can be
used to determine the lengths of the sides of a right triangle. Explain your thinking.
20
18
16
14
12
10
8
6
4
2
0
2
4
6
8
10
12
14
16
18
20
15. Determine the value of a in the diagram below. Show your work and label your answer. If
your answer is not rational then state which two integers it is between.
b  8inches
a?
Math 8 Practice Test
c  10inches
Unit 07B: Roots and The Pythagorean Theorem
Revised 2012 - CCSS
Page 3 of 5
16. (MCAS) The roads connecting the three towns on the map below form a right triangle. Two
of the distances are given in the diagram below.
Rosewood
17 km
15km
Daisy
Lily
?
Based on the distances given on the map, what is the distance between Daisy and Lily?
A. 2 km
B. 8 km
C. 15 km
D. 32 km
17. Juana was walking on the beach when she found a map. The map said to walk 8 meters due
North, then 7 meters due East, and finally 3 meters due South. Sketch Juana’s route on the
grid and answer the question below.
What is the shortest distance back to where Juana found the map? Show your work or
explain your thinking.
meters
10
8
Map
6
4
2
0
Math 8 Practice Test
2
4
6
8
10 meter
meters
Unit 07B: Roots and The Pythagorean Theorem
Revised 2012 - CCSS
Page 4 of 5
18. Listed below are the three side lengths of a triangle. Which of the following is NOT a right
triangle?
A.
B.
C.
D.
3 in, 4 in, 5 in
6 ft, 7 ft, 8 ft
5 m, 12 m, 13 m
8 cm, 15 cm, 17 cm
19. (CRT) The hypotenuse of a right triangle is 392 centimeters long. The legs of the triangle
have equal lengths, as shown in the diagram below.
392
What is the length of each leg?
A.
196 cm
B.
300 cm
C.
14 cm
D.
92 cm
Long Term Memory Review:
For problems 20 and 21, simplify. Show your work.
1
3
20. 2  5
2
4
21.
5
1
 ( )
8
4
p
22. Use the diagram to answer the question below.
t°
Determine w° given q  r line and t  63 . Justify your answer.
w°
q
r
Math 8 Practice Test
Unit 07B: Roots and The Pythagorean Theorem
Revised 2012 - CCSS
Page 5 of 5