1. Square Root

2. Learning Intention/Success Criteria
LI: We are learning to use and simplify square roots SC: I can -use integer operations -use square roots -solve multi-step equations -simplify square roots -find square number factors

3. Example 1: Show that the given number has a perfect square factor90 90
1 90
2 45
3 30
5 18
6 15
9 10

4. Poll Show that the given number has a perfect square factor 75
A] B] C] D] Prime

5. Guided Practice 1
Show that the given number has a perfect square factor 75
1 75
3 25
5 15

6. Poll Show that the given number has a perfect square factor 200
A] B] C] D] E] F]

7. Guided Practice 2
Show that the given number has a perfect square factor
200
1 200
2 100
4 50
5 40
8 25
10 20

8. Poll Show that the given number has a perfect square factor 12
A] B] 2 6 C] 3 4 D] Prime

9. Guided Practice 3
Show that the given number has a perfect square factor 12
1 12
2 6
3 4

10. Example 2: Write an equivalent expression for the following:𝟐𝟎 𝟐𝟎
= 𝟒•𝟓
= 𝟒 • 𝟓
=𝟐 𝟓

11. Poll Write an equivalent expression for the following:
𝟗𝟎 A] 𝟑 𝟏𝟎 𝐁] 𝟗 𝟏𝟎 𝐂] 𝟏𝟎 𝟑 𝐃] 𝟏𝟎 𝟗 E] 𝟗𝟎 , it’s simplified

12. Guided Practice 4 Write an equivalent expression for the following: 𝟗𝟎
= 𝟗•𝟏𝟎
= 𝟗 • 𝟏𝟎
=𝟑 𝟏𝟎

13. Poll Write an equivalent expression for the following: 𝟕𝟓
A] 5 𝟓 𝐁] 𝟑 𝟓 𝐂] 𝟓 𝟑 𝐃] 𝟕𝟓 ; can’t be simplified

14. Guided Practice 5 Write an equivalent expression for the following: 𝟕𝟓
= 𝟐𝟓•𝟑
= 𝟐𝟓 • 𝟑
=𝟓 𝟑

15. Poll Write an equivalent expression for the following:
𝟐𝟎𝟎 A] 5 𝟖 𝐁] 𝟏𝟎 𝟐 𝐂] 𝟐 𝟏𝟎 𝐃] 𝟖 𝟓 𝑬] 𝟐𝟎𝟎 ; it’s simplified

16. Guided Practice 6 Write an equivalent expression for the following:
𝟐𝟎𝟎
= 𝟏𝟎𝟎•𝟐
= 𝟏𝟎𝟎 • 𝟐
=𝟏𝟎 𝟐

17. Example 3: Write an equivalent expression for the following:
𝟔𝟎𝟎 𝟐
𝟔𝟎𝟎 𝟐
𝟏𝟎𝟎∙𝟔 𝟐
𝟏𝟎𝟎 ∙ 𝟔 𝟐
𝟏𝟎 𝟔 𝟐
5 6

18. Guided Practice 7 Write an equivalent expression for the following:
𝟑𝟎𝟎 𝟐
𝟏𝟎𝟎∙𝟑 𝟐
𝟏𝟎𝟎 ∙ 𝟑 𝟐
𝟏𝟎 𝟑 𝟐
5 3

19. Guided Practice 8 Write an equivalent expression for the following:
𝟒𝟎 𝟖
𝟒∙𝟏𝟎 𝟖
𝟒 ∙ 𝟏𝟎 𝟖
𝟐 𝟏𝟎 𝟖
𝟏𝟎 𝟒

20. Guided Practice 8 Write an equivalent expression for the following:
𝟐𝟓𝟎 𝟐
𝟐𝟓∙𝟏𝟎 𝟐
𝟐𝟓 ∙ 𝟏𝟎 𝟐
𝟓 𝟏𝟎 𝟐

21. Guided Practice 9 Write an equivalent expression for the following:
𝟑𝟐 𝟐
𝟏𝟔∙𝟐 𝟐
𝟏𝟔 ∙ 𝟐 𝟐
𝟒 𝟐 𝟐
2 2

22. Example 4: Solve for x 3x2 – 300 = 0 3x2 – 300 = 0 + 300 + 300
______________
___ 3
3x2 = 300
___ 3
x2 =
x =  10
Check Your Work:
3x2 – 300 = 0
3x2 – 300 = 0
3(-10)2 – 300 = 0
3(10)2 – 300 = 0
300 – 300 = 0
300 – 300 = 0
0 = 0
0 = 0

23. Poll Solve the following equation: x2 – 144 = 0
A] x = 72, - 72 B] x = 12, - 12 C] x = 144, -144 D] x = 0

24. Guided Practice 9 Solve the following equation: x2 – 144 = 0
Check With Work:
x2 – 144 = 0
+ 144
+ 144
(12)2 – 144 = 0
______________
144 – 144 = 0
x2 =
0 = 0
x =  12
x2 – 144 = 0
(-12)2 – 144 = 0
144 – 144 = 0
0 = 0

25. Poll Solve the equation:
5x2 – 20 = 0 A] x = 2, -2 B] x = 4, -4 C] x = 5, -5 D] x = 0

26. Guided Practice 10 Check With Work: Solve the equation: 5x2 – 20 = 0
5(2)2 – 20 = 0
5(4) – 20 = 0
+ 20
+ 20
______________
20 – 20 = 0
5x2 = 20
___ 5
___ 5
0 = 0
5x2 – 20 = 0
5(-2)2 – 20 = 0
x2 = 4
5(4) – 20 = 0
x =  2
20 – 20 = 0
0 = 0

27. Example 5: Solve for x (x + 5)2 = 24
- 5
- 5
______________________
x = -5

28. Guided Practice 11 Solve the equation: (x – 7)2 = 81 x – 7 = ± 9 + 7
________________
x = 7 ± 9
x = 7 + 9
x = 7 - 9
x = 16
x = - 2

29. Guided Practice 12 Solve the equation: (x – 8)2 = 50 x – 8 = x – 8 =
+ 8
________________
+ 8
x =