1. 81
Squares
What is this shape?
How do you know?
What is the area?
How many small squares are
inside the large square?
What is the perimeter?

2. Perfect Square Activity

3. What is a Root?

4. 81
Squares
What is a root?
What is the area of
this square?
What is the root?
Is there any other number 4
Multiplied by itself that equals
16?

5. Perfect Squares
• 0 x 0 = 02 = 0
• 1 x 1 = 12 = 1 -1 x -1 = (-1)2 = 1
• 2 x 2 = 22 = 4 -2 x -2 = (-2)2 = 4
• 3 x 3 = 32 = 9 -3 x -3 = (-3)2 = 9
• 4 x 4 = 42 = 16 -4 x -4 = (-4)2 = 16
• 5 x 5 = 52 = 25 -5 x -5 = (-5)2 = 25
• 6 x 6 = 62 = 36 -6 x -6 = (-6)2 = 36
• 7 x 7 = 72 = 49 -7 x -7 = (-7)2 = 49
• 8 x 8 = 82 = 64 -8 x -8 = (-8)2 = 64
• 9 x 9 = 92 = 81 -9 x -9 = (-9)2 = 81
• 10 x 10 = 102 = 100 -10 x -10 = (-10)2 = 100

6. 4 =2
16 =4
25 =5
100 = 10
144 = 12

7. Notes
• The root of a square (square root) is equal
to the length of one side of the square
• All squares have two roots, one positive
and one negative
• Perfect squares have integers for roots
• A Radical is the symbol we use to identify
roots
• A Radicand is the number or variable
inside the radical 25

8. Perfect Squares
1 64 225
4 81 256
9 100 289
16 121 324
25 144 361
36 169 400
49 196 625

9. Estimating Non-Perfect Squares
• Squares that do not have an integer for a base are
called non-perfect squares. For example 20 is a
non-perfect square because no integer multiplied by
itself equals 20.
• We estimate non-perfect squares by finding which
perfect squares they are between:
16 20 25
4 4.5 5
0 1 2 3 4 5 6 7 8 9 10 11 12
16 25

10. Non-Perfect Squares

11. Let’s Practice
Plot:
1. 6 4. 15
2. 30 5. 90
3. 55 6. 75
0 1 2 3 4 5 6 7 8 9 10

12. Perfect Cubes

13. Perfect Cubes
• How do you find the volume of a cube?
2cm

14. Perfect Cubes
• How do you find the root of a cube?
8cm3

15. Perfect Cubes
• What is the volume of this cube?
• What is the root of this cube?

16. Perfect Cubes
• What is the volume of this cube?
• What is the root of this cube?

17. Perfect Cubes
• What is the volume of this cube?
• What is the root of this cube?

18. Let’s Practice

19. Notes

20. Perfect Cubes
1 -1
8 -8
27 -27
64 -64
125 -125
216 -216
343 -343
512 -512
729 -729
1000 -1000