SECTION 3-8
Equations with Squares and Square Roots

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

VOCABULARY
1. Inverse of an Operation:

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

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

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

QUESTION
What is the opposite of squaring?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

EXAMPLE 2
3
7.91×10 = 9.8r

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

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

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

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

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

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.

HOMEWORK

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