The document is focused on teaching grade 8 students about square numbers and square roots through various exercises and examples. It includes definitions, explanations, and problems for students to solve regarding identifying square numbers, calculating factors, and determining side lengths of squares based on area. Additionally, it highlights the relationship between square numbers and their factors, emphasizing that a number with an odd number of factors is a square number.

1. From Square Numbers
to Square Roots
Grade 8 Mathematics
Mr. J. Lingley

2. Square # Review
These numbers below are not square numbers.
Which two consecutive square numbers is each
number between?
12
40
75
200
How do you know?

3. Square # Review
The floor of a large square room has an area of
144 m2. What is the length of a side of the
room? How much baseboard is needed to go
around the room?

4. Square # Review
The floor of a large square room has an area of
144 m2. What is the length of a side of the
room? How much baseboard is needed to go
around the room?

5. Is there a shorter way to find the side length?

6. 144

7. What the
heck is that?
144

8. Square Roots
The square root ( ) of a number finds the
factor that when multiplied by itself will give
you the square number. In other words it goes
from area to side length. Back to the root.
144 = 12 122 = 144
A square root and a square are opposite operations.

9. Even donald knows something about square roots.

10. Exploring Square Roots
Fun With Squares and Square roots!
Name: Date: ! ! ! ! Class:
In class we have been observing that any
whole number multiplied by itself will give
us a square number. Now it’s time to look
at what the factors of those square
numbers tell us.
Factor: A number that divides exactly into
another number. For example, 1,2,3 and 6
are factors of 6.
What are all of
the factors of 10?
Please help!
Investigate!
Working with a partner, complete the table below. Indicate all of the factors for a given
whole number along the bottom of the table. Remember, that if a number multiplied by
itself gives you the target whole number, only copy down that factor once. For
instance: 9 = 3 x 3, however the factors for 9 are: 1, 3, 9 - not 1, 3, 3, 9.

11. us a square number. Now it’s time to look
at what the factors of those square
numbers tell us.
Factor: A number that divides exactly into
another number. For example, 1,2,3 and 6
are factors of 6.
Please help!
Exploring Square Roots
Investigate!
Working with a partner, complete the table below. Indicate all of the factors for a given
whole number along the bottom of the table. Remember, that if a number multiplied by
itself gives you the target whole number, only copy down that factor once. For
instance: 9 = 3 x 3, however the factors for 9 are: 1, 3, 9 - not 1, 3, 3, 9.
6 8
4 3 4
2 3 2 5 2 7 2
1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
start here!
Questions:
Calculators are permitted.

12. instance: 9 = 3 x 3, however the factors for 9 are: 1, 3, 9 - not 1, 3, 3, 9.
6 8
4 3 4
2 3 2 5 2 7 2
1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
start here!
Questions:
1. Which numbers have only two factors? What do you notice about these numbers?
2. Which numbers have an even number of factors, but more than 2 factors?
3. Which numbers have an odd number of factors?

13. Odd # of Factors Even # of Factors

14. Odd # of Factors Even # of Factors
square number
When a number has an odd
number of factors, it is a square
number.
36 = 1, 2, 3, 4, 6, 9, 12, 18, 36 9 Factors
The square number can be
always found in the middle.

15. Fill in this table...
Square Root Square Number
4
64
144
7
13
100

16. Your Turn
1. The factors of 136 are listed in ascending order.
136 = 1, 2, 4, 8, 17, 34, 68, 136
Is 136 a square number?
2. Find:
42 62 82 72 92 12
25 64 81
162