Students will use their understanding of square numbers to evaluate square roots. Remember, square roots, quite literally mean going from square numbers, back to the root - the number which you multiplied in the first place to get the square number. Example: The square root of 49 is 7.

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