Equations with Squares and Square Roots

1. SECTION 3-8
Equations with Squares and Square Roots

2. ESSENTIAL QUESTIONS
• How do you solve problems involving squares?
• How do you solve problems involving square roots?
• Where you’ll see this:
• Physics, safety, engineering, mechanics

3. VOCABULARY
1. Inverse of an Operation:

4. VOCABULARY
1. Inverse of an Operation: The opposite of an operation

5. VOCABULARY
1. Inverse of an Operation: The opposite of an operation
Addition and subtraction

6. VOCABULARY
1. Inverse of an Operation: The opposite of an operation
Addition and subtraction
Multiplication and division

7. QUESTION
What is the opposite of squaring?

8. EXAMPLE 1
Solve each equation. Check the solution.
2 4
a. x = 2
b. x − 225 = 0
9

9. EXAMPLE 1
Solve each equation. Check the solution.
2 4
a. x = 2
b. x − 225 = 0
9
2 4
x =±
9

10. EXAMPLE 1
Solve each equation. Check the solution.
2 4
a. x = 2
b. x − 225 = 0
9
2 4
x =±
9
2
x=±
3

11. EXAMPLE 1
Solve each equation. Check the solution.
2 4
a. x = 2
b. x − 225 = 0
9 +225 +225
2 4
x =±
9
2
x=±
3

12. EXAMPLE 1
Solve each equation. Check the solution.
2 4
a. x = 2
b. x − 225 = 0
9 +225 +225
2
2 4 x = 225
x =±
9
2
x=±
3

13. EXAMPLE 1
Solve each equation. Check the solution.
2 4
a. x = 2
b. x − 225 = 0
9 +225 +225
2
2 4 x = 225
x =±
9 2
x = ± 225
2
x=±
3

14. EXAMPLE 1
Solve each equation. Check the solution.
2 4
a. x = 2
b. x − 225 = 0
9 +225 +225
2
2 4 x = 225
x =±
9 2
x = ± 225
2 x = ±15
x=±
3

15. EXAMPLE 1
Solve each equation. Check the solution.
2
c. 3 x +1= 3 d. 24 = v

16. EXAMPLE 1
Solve each equation. Check the solution.
2
c. 3 x +1= 3 d. 24 = v
−1 −1

17. EXAMPLE 1
Solve each equation. Check the solution.
2
c. 3 x +1= 3 d. 24 = v
−1 −1
3 x =2

18. EXAMPLE 1
Solve each equation. Check the solution.
2
c. 3 x +1= 3 d. 24 = v
−1 −1
3 x =2
3 3

19. EXAMPLE 1
Solve each equation. Check the solution.
2
c. 3 x +1= 3 d. 24 = v
−1 −1
3 x =2
3 3
2
x=
3

20. EXAMPLE 1
Solve each equation. Check the solution.
2
c. 3 x +1= 3 d. 24 = v
−1 −1
3 x =2
3 3
2
x=
3
2
2  2
( x) = 
 3

21. EXAMPLE 1
Solve each equation. Check the solution.
2
c. 3 x +1= 3 d. 24 = v
−1 −1
3 x =2
3 3
2
x=
3
2
2  2 4
( x) = 
 3
x=
9

22. EXAMPLE 1
Solve each equation. Check the solution.
2
c. 3 x +1= 3 d. 24 = v
−1 −1
2
± 24 = v
3 x =2
3 3
2
x=
3
2
2  2 4
( x) = 
 3
x=
9

23. EXAMPLE 1
Solve each equation. Check the solution.
2
c. 3 x +1= 3 d. 24 = v
−1 −1
2
± 24 = v
3 x =2
3 3 v = ± 24
2
x=
3
2
2  2 4
( x) = 
 3
x=
9

24. EXAMPLE 1
Solve each equation. Check the solution.
2
c. 3 x +1= 3 d. 24 = v
−1 −1
2
± 24 = v
3 x =2
3 3 v = ± 24
2
x= or
3
2
2  2 4
( x) = 
 3
x=
9

25. EXAMPLE 1
Solve each equation. Check the solution.
2
c. 3 x +1= 3 d. 24 = v
−1 −1
2
± 24 = v
3 x =2
3 3 v = ± 24
2
x= or
3
2  2
2
4 v ≈ ±4.898979486
( x) = 
 3
x=
9

26. EXAMPLE 1
Solve each equation. Check the solution.
2
e. c = f. 7w −10 = 4
3

27. EXAMPLE 1
Solve each equation. Check the solution.
2
e. c = f. 7w −10 = 4
3
2
2  2
( c) = 
 3

28. EXAMPLE 1
Solve each equation. Check the solution.
2
e. c = f. 7w −10 = 4
3
2
2  2
( c) = 
 3
4
c=
9

29. EXAMPLE 1
Solve each equation. Check the solution.
2
e. c = f. 7w −10 = 4
3 +10 +10
2
2  2
( c) = 
 3
4
c=
9

30. EXAMPLE 1
Solve each equation. Check the solution.
2
e. c = f. 7w −10 = 4
3 +10 +10
2
2  2 7w =14
( c) = 
 3
4
c=
9

31. EXAMPLE 1
Solve each equation. Check the solution.
2
e. c = f. 7w −10 = 4
3 +10 +10
2
2  2 7w =14
( c) = 
 3 2
( 7w ) =14 2
4
c=
9

32. EXAMPLE 1
Solve each equation. Check the solution.
2
e. c = f. 7w −10 = 4
3 +10 +10
2
2  2 7w =14
( c) = 
 3 2
( 7w ) =14 2
4
c= 7w =196
9

33. EXAMPLE 1
Solve each equation. Check the solution.
2
e. c = f. 7w −10 = 4
3 +10 +10
2
2  2 7w =14
( c) = 
 3 2
( 7w ) =14 2
4
c= 7w =196
9 7 7

34. EXAMPLE 1
Solve each equation. Check the solution.
2
e. c = f. 7w −10 = 4
3 +10 +10
2
2  2 7w =14
( c) = 
 3 2
( 7w ) =14 2
4
c= 7w =196
9 7 7
w = 28

35. EXAMPLE 2
The velocity v of a satellite moving in a circular orbit near the
surface of Earth is given by the formula v = gr ,
where g represents the force of gravity and r represents the
radius of Earth. Given that g = 9.8 m/sec2 and v = 7.91X103
m/sec, determine the radius of Earth to the nearest meter.

36. EXAMPLE 2
The velocity v of a satellite moving in a circular orbit near the
surface of Earth is given by the formula v = gr ,
where g represents the force of gravity and r represents the
radius of Earth. Given that g = 9.8 m/sec2 and v = 7.91X103
m/sec, determine the radius of Earth to the nearest meter.
v = gr

37. EXAMPLE 2
The velocity v of a satellite moving in a circular orbit near the
surface of Earth is given by the formula v = gr ,
where g represents the force of gravity and r represents the
radius of Earth. Given that g = 9.8 m/sec2 and v = 7.91X103
m/sec, determine the radius of Earth to the nearest meter.
v = gr
3
7.91×10 = 9.8r

38. EXAMPLE 2
3
7.91×10 = 9.8r

39. EXAMPLE 2
3
7.91×10 = 9.8r
7910 = 9.8r

40. EXAMPLE 2
3
7.91×10 = 9.8r
7910 = 9.8r
2
2
7910 = ( 9.8r )

41. EXAMPLE 2
3
7.91×10 = 9.8r
7910 = 9.8r
2
2
7910 = ( 9.8r )
62568100 = 9.8r

42. EXAMPLE 2
3
7.91×10 = 9.8r
7910 = 9.8r
2
2
7910 = ( 9.8r )
62568100 = 9.8r
9.8 9.8

43. EXAMPLE 2
3
7.91×10 = 9.8r
7910 = 9.8r
2
2
7910 = ( 9.8r )
62568100 = 9.8r
9.8 9.8
r = 6384500

44. EXAMPLE 2
3
7.91×10 = 9.8r
7910 = 9.8r
2
2
7910 = ( 9.8r )
62568100 = 9.8r
9.8 9.8
r = 6384500
The radius of Earth is about 6384500 meters.

45. HOMEWORK

46. HOMEWORK
p. 138 #1-51 odd
“If fifty million people say a foolish thing, it is still a foolish
thing.” - Anatole France