1. Square Roots and Solving Quadratics with Square Roots
Review

2. GET YOUR COMMUNICATORS!!!!

3. Warm Up
Simplify. 25 64
144
225
5. 202
400

4. Perfect Square A number that is the square of a whole number
Can be represented by arranging objects in a square.

5. Perfect Squares

6. Perfect Squares
1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16

7. Perfect Squares 1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 4 x 4 = 16 Activity:
Calculate the perfect
squares up to 152…

8. Perfect Squares 1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 4 x 4 = 16 5 x 5 = 25

9. Activity: Identify the following numbers as perfect squares or not.16 15
146
300
324
729

10. Activity: Identify the following numbers as perfect squares or not.
16 = 4 x 4 15
146
300
324 = 18 x 18
729 = 27 x 27

11. Perfect Squares: Numbers whose square roots are integers or quotients of integers.

12. Perfect Squares
One property of a perfect square is that it can be represented by a square array.
Each small square in the array shown has a side length of 1cm.
The large square has a side length of 4 cm.
4cm
4cm
16 cm2

13. Perfect Squares The large square has an area of 4cm x 4cm = 16 cm2.
The number 4 is called the square root of 16.
We write: 4 =
4cm
4cm
16 cm2

14. Square Root
A number which, when multiplied by itself, results in another number.
Ex: 5 is the square root of 25.
5 = 25

15. Finding Square Roots 36 = ___ x ___
We can think “what” times “what” equals the larger number.
= ___ x ___ -6 -6 6 6
Is there another answer?
SO ±6 IS THE SQUARE ROOT OF 36

16. Finding Square Roots 256 = ___ x ___
We can think “what” times “what” equals the larger number.
= ___ x ___ 16
-16
-16 16
Is there another answer?
SO ±16 IS THE SQUARE ROOT OF 256

17. Estimating Square Roots
25 = ?

18. Estimating Square Roots
25 = ±5

19. Estimating Square Roots
= ?

20. Estimating Square Roots
= -7
IF THERE IS A SIGN OUT FRONT OF THE RADICAL
THAT IS THE SIGN WE USE!!

21. Estimating Square Roots
27 = ?

22. Estimating Square Roots
27 = ?
Since 27 is not a perfect square, we will leave it in a radical because that is an EXACT ANSWER.
If you put in your calculator it would give you 5.196, which is a decimal apporximation.

23. Estimating Square Roots
Not all numbers are perfect squares.
Not every number has an Integer for a square root.
We have to estimate square roots for numbers between perfect squares.

24. Estimating Square Roots
To calculate the square root of a non-perfect square
1. Place the values of the adjacent perfect squares on a number line.
2. Interpolate between the points to estimate to the nearest tenth.

25. Estimating Square Roots
Example:
What are the perfect squares on each side of 27? 25 30 35 36

26. Estimating Square Roots
Example:
half 5 6 25 30 35 36 27
Estimate = 5.2

27. Estimating Square Roots
Example:
Estimate: = 5.2
Check: (5.2) (5.2) = 27.04

28. Find the two square roots of each number.
49 = 7
7 is a square root, since 7 • 7 = 49.
49 = –7
–7 is also a square root, since –7 • –7 = 49.
B. 100
100 = 10
10 is a square root, since 10 • 10 = 100.
100 = –10
–10 is also a square root, since –10 • –10 = 100.
C. 225
225 = 15
15 is a square root, since 15 • 15 = 225.
225 = –15
–15 is also a square root, since –15 • –15 = 225.

29. Find the two square roots of each number.
25 = 5
5 is a square root, since 5 • 5 = 25.
25 = –5
–5 is also a square root, since
–5 • –5 = 25.
B. 144
144 = 12
12 is a square root, since 12 • 12 = 144.
144 = –12
–12 is also a square root, since
–12 • –12 = 144.
C. 289
17 is a square root, since 17 • 17 = 289.
289 = 17
289 = –17
–17 is also a square root, since
–17 • –17 = 289.

30. Evaluate a Radical Expression
EXAMPLE SHOWN BELOW

31. Evaluate a Radical Expression#1

32. Evaluate a Radical Expression#2

33. Evaluate a Radical Expression#3

34. Evaluate a Radical Expression#4

35. SOLVING EQUATIONS
SOLVING MEANS “ISOLATE” THE VARIABLE
x = ??? y = ???

36. Solving quadratics Solve each equation.
SQUARE ROOT BOTH SIDES
Solve each equation.
a. x2 = 4 b. x2 = 5 c. x2 = d. x2 = -1

37. Solve
Solve 3x2 – 48 = 0
3x2 = 48
x2 = 16

38. Example 1: Solve the equation: 1.) x2 – 7 = 9 2.) z2 + 13 = 5
z2 = -8
x2 = 16

39. Example 2:
Solve 9m2 = 169
m2 =

40. Example 3:
Solve 2x2 + 5 = 15
2x2 = 10
x2 = 5

41. Example: 2. 1.
x2 = 36
x2 = 25

42. Example: 3.
4x2 = 48
x2 = 12

43. Examples: 4. 5.
-5x2 = -12
4 4
x2 = 104
x2 = 12/5