1. SQUARES
&
SQUARE ROOTS

2. Introduction Explore the Math- page 80 Questions 1-5
Working in groups of 3.

3. Introduction
Talk in your groups about the following questions. Be prepared to discuss them if I call on you.
The numbers 1, 4, 9, 16, 25, etc. are known as perfect squares. Why do you think they are called perfect squares?
How could you find the next numbers that are perfect squares without tiles or prime factorization?

4. Introduction
Try This Write down the first 10 perfect squares, starting with 0. 0, 1, 4, 9, ___, ___, ___, ___, ___, ___ Now subtract each number from the one after it. 1 , 3 , 5 , ___, ___, ___, ___, ___ What pattern do you see in the difference between two perfect squares? Use your answer from Exercise 3 above to find all perfect squares less than 200.

5. Math outcome
Demonstrate an understanding of perfect squares and square roots.

6. Squares
“Squaring” a number means to raise a number to the second power.
A square number is the product of the same two numbers. 3x3=9, so 9 is a square number.
Example:
4² = 4 · 4 = 16
9² = 9 · 9 = 81
16² = 16 · 16 = 256

7. Squares
There are many ways to determine if a number is a square number. 1.If you can write a division sentence for a number so that the quotient is equal to the divisor, the number is a square number. ex. 9 ÷ 3 = 3

8. Squares
2. You can also use prime factorization.Prime factorization is when a number is written as the product of its prime factors.

9. Squares
3.Can be represented by arranging objects in a square.

10. Square Roots
The square root of a number is the number you can multiply by itself to give you that number.
Example:
= 2, because 22=4
= 3, because 32=9

11. Square Roots Try: = 8, because 82=64 = 12, because 122=144

12. Perfect Squares
A perfect square is “perfect” because its square root is a whole number.
Example:
is a perfect square because = 49 7

13. Non-Perfect squares Example: is NOT a perfect square because= 40
A non-perfect square is a number whose square root is NOT a whole number.
Example:
is NOT a perfect square because= 40
6.3245…

14. Practice Problems
Page 85
Questions- 4-16

15. Jigsaw Page 86/87 Group 1: Questions 17 & 25

16. Math outcome
Determine the approximate square root of numbers that are not perfect squares.

17. Approximating square roots
To estimate the value of non-perfect squares by determining which two perfect squares it falls in between.
Example:
11 is a non-perfect square
11 falls between perfect squares 9 & 16
Therefore, is between and
Since, = 3 and = 4
Then is between 3 and 4

18. Find the two consecutive whole numbers the following non-perfect square fall between. SHOW WORK!
√55 
√23
√5 
√14
√44
and
Between 7 & 8
and
Between 4 & 5
and
Between 2 & 3
and
Between 3 & 4
Between 6 & 7
and

19. Extension Questions Show Your Work!
I am a number. I am not zero. If I am squared, I’m still the same number. What number am I? 1

20. If a square bedroom has an area of 144 square meters, what is the length of one wall?20

21. 3. A square garden has an area of 225 square meters
3. A square garden has an area of 225 square meters. How much fencing will a gardener need to buy in order to place fencing around the garden?
60 meters 21

22. Individual Practice
Page 99
Questions 4,5,6,10,11,13