1. Squares, Cubes and Roots
8th Grade Math 2013-14
MCC8EE2, MCC8NS1, MCC8NS2

2. POD 17 Sep
Evaluate
1. –122
2. (a4b3)(a5b2)
Simplify; write solution in Scientific Notation:
3. 3 x 10-3 • 4 x 104
4. .00065 x 103

3. POD 18 Sep
Use the information given to find the measures of:
1. angle d
l1 || l2 and l3 || l4
l1
l2
l3 l4
a
b
c
de
f
g
h
j ki
540

4. 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?
8181

5. Perfect Square Activity

6. What is a Root?

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

8. 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

9. 4
16
25
100
144
= 2
= 4
= 5
= 10
= 12

10. 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

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

12. Estimating Non-Perfect Squares
0 5 101 2 3 4 12119876
• Squares that do not have an integer for a base are
called non-perfect squares. For example 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:
20
2016 25
16 25
4 55.4

13. Non-Perfect Squares

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

15. Perfect Cubes

16. Perfect Cubes
2cm

17. Perfect Cubes
• How do you find the root of a cube?
• The length of 1 side of a square is the
square root, and the length of 1 side of a
cube is the cube root
8cm3

18. Perfect Cubes

19. Perfect Cubes

20. Perfect Cubes

21. Let’s Practice

22. Notes

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

24. Compare Numbers