Date: ________________
Name: __________________
MMS 8 Chapter 1 Unit Test A
1. Use a diagram to show that each number below is a square number.
a) 121
b) 900
30 cm
11 cm
11 cm
30 cm
2. Find the side length of a square with each area. Show how you know.
a) 100 cm²
__10 x 10 = 100___therefore 10 is the square root___
b) 64 cm²
__8 x 8 = 64___therefore 8 is the square root__
c) 400 m²
__20 x 20 = 400___therefore 20 is the square root__
3. I am a square number. The sum of my digits is 9. What square
numbers might I be? (list at least 2 possibilities)
___36 or 81____
4. Which whole numbers between 50 and 200 are perfect squares?
Explain how you know.
____64, 81, 100, 121, 144, 169, 196 are all perfect squares because when
you take a whole number and times it by itself you get these products –
the numbers to multiply together are: 8, 9, 10, 11, 12, 13, 14____
5. Find. (show your work)
a) 8²
____8 x 8 = 64______
b) 3²
____3 x 3 = 9_____
Find a square root of each number. (Show your proof)
a) 25
____5 x 5 = 25 so 5 is the square root 25_____
b) 64
_____8 x 8 = 64 so 8 is the square root of 64____
6. Use a table to list factor pairs, or list factors in ascending order for
the following numbers.
a) 500
500
500
250
125
100
50
25
1
2
4
5
10
20
b) 85
85
85
17
1
5
7. Find each square root. Use a table, list or diagram to support your
answer.
a) √36
b) √144
12
6
12
6
1
2
3
4
6
36
36
18
12
9
6
1
2
3
4
6
8
9
12
144
144
72
48
36
24
18
16
12
8. Find the area of the square. Then write the side length of the square.
Remember to show your work
Area of Big Square: _16 units____
Area of 1 Triangle: __1 ½ units²____
Area of 4 Triangles: __6 units ²____
Area of Inside Square: _10 units ²_
Side Length of Inside Square:
___√10____
Rough work space:
4 x 4 = 16
(3x1) / 2 = 1.5 units squared
1.5 x 4 = 6 units squared
16 – 6 = 10 units squared
9. Between which two consecutive whole numbers is each square root?
a) √5
___2 and 3___
b) √11
___3 and 4___
c) √115 ___10 and 11_____
10. Place each square root on the number line to show its approximate
value.
a) √30
b) √55
√17
3
4
c) √17
√30
5
√55
6
7
8
11. Find the approximate side length of the square with each area. Give
your answer to one decimal place. (Show your work / proof)
a) 92 cm²
__√81 = 9 and √100 = 10 so √92 is about 9.5 __
b) 150 cm²
__√144 = 12 and √169 = 13 so √150 is about 12.2__
12. Find the length of each hypotenuse. (Show your work)
a)
6
8
b)
3
5
Work Space
6x6+8x8
36 + 64 = 100
√100 is 10
Answer
Work Space
3x3+5x5
9 + 25 = 34
√34 = h
Answer
10
units
√34
units
13. Find the length of each leg marked L.
a)
15
12
L
b)
L
26
10
Work Space
15 x 15 – 12 x 12
225 – 144 = 81
√81 = 9
Answer
Work Space
26 x 26 - 10 x 10
676 – 100 = 576
√576 = 24
Answer
9 units
24
units
14. Find the length of the diagonal, D, in this diagram
a)
Work Space
24
24 x 24 + 7 x 7
D
576 + 49 = 625
√625 = 25
Answer
25
7
15. Which of the following sets of numbers are Pythagorean Triples?
Show how you determined if they are or not.
Number Set
a) 16, 30, 34
b) 6, 8, 9
c) 9, 30, 35
Work Space
16 x 16 + 30 x 30 = 256 +900 = 1156
34 x 34 = 1156
Yes it is a Pythagorean triple
6 x 6 + 8 x 8 = 36 + 64 = 100
9 x 9 = 81
No, not a Pythagorean triple
9 x 9 + 30 x 30 = 81 + 900 = 981
35 x 35 = 1225
No, not a Pythagorean triple
16. Is this triangle a right triangle? Justify your answer (show your
proof)
Work Space
Answer
7 x 7 + 10 x 10 = 49 + 100
49 + 100 = 149
Not a
13
13 x 13 = 169
right
10
triangle
7
17. A baseball diamond is a square with side lengths of about 27m. The
player throws the ball from second base to home plate. How far did
the player throw the ball? Give your answer to one decimal point.
Remember to show your work. You may want to draw a diagram.
27 x 27 + 27 x 27 = 729 + 729 = 1458
√1458 = 38.2
18. Find the length of the line segment. (hint you’ll need to make a
triangle… )
a)
7 x 7 + 2 x 2 = 49 + 4 = 54
√54 = 7.3 = line segment
19. Two cars begin at the same intersection. One travels north at a speed
of 80 km/hour. The other car travels East at a speed of 55 km/hour.
How far apart are the two cars after 3 hours? Give your answer to
one decimal point. (Hint: remember you are trying to make a triangle,
make a diagram or picture)
Car A – 80 x 3 = 240km
Car B – 55 x 3 = 165km
240 x 240 + 165 x 165 = 57,600 + 27,225 = 84825
√84825 = 291.25
They are approximately 291 km apart after 3 hours