Solve Each Equation by using Square Root Property (10 POINTS!)

Write All Radicals in Simplest Form

1. x² = 81

2. r² + 36 = 0

3. y² - 250 = 0

4. (x-9)² = 49

5. (m+12)² = -9

6. (2x+9)² -4 = 0

7. (3r - 2)² - 28 = 0

√(ab) = √a * √b

x² = 81
x = +/- √81
x = 9,-9

r² + 36 = 0
r² = -36
r = +/- √-36
r = 6i,-6i,

y² - 250 = 0
y² = 250
y = +/- √250
y = +/- √(25 * 10)
y = 5/- 5√10

(x-9)² = 49
x-9 = 7,-7
x = 16, 2

(m+12)² = -9
m+12 = 3i,-3i
m = 3i - 12, -3i - 12

(2x+9)² -4 = 0
(2x+9)² = 4
2x+9 = 2,-2
2x = -7, -11
x = -7/2 , -11/2

(3r - 2)² - 28 = 0
(3r - 2)² = 28
3r - 2 = +/- √28
3r - 2 = +/- √(4 * 7)
3r - 2 = +/- 2√7
3r = 2 +/- 2√7
r = (2 +/- 2√7 )/3

x^2 = 81

√x^2 = +/- √81

x = +/- 9




r^2 = -36

√r^2 = +/- √-36

r = +/- (√36 x √-1)

r = +/- 6 x i

r = +/- 6i




y^2 = 250

√y^2 = +/- √250

y= +/- (√(25x10))

y= +/- 5√10








(x-9)^2 = 49

x - 9 = +/- √49

x = 9 +/- 7

x1 = 9 - 7

x1 = 2

x2 = 9 + 7

x2 = 16

THEREFORE x= -2, 16







(m+12)^2 = -9

m + 12 = +/- √-9

m = -12 +/- 3i






(2x+9)^2 = 4

2x+9 = +/- √4

2x = -9 +/- 2

x = (-9 +/- 2)/2

x1 = (-9 -2)/2

x1 = -11/2

x2 = (-9 +2)/2

x2 = -7/2

THEREFORE x= -11/2, -7/2






(3r-2)^2 = 28

3r - 2 = +/- √28

3r = 2 +/- √(4x7)

r = (2 +/- 2√7)/3