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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________
Solving Quadratic Equations with Square Roots
Solve each equation by taking square roots.
1)
k
2
= 76 2)
k
2
= 16
3)
x
2
= 21 4)
a
2
= 4
5)
x
2
+ 8 = 28 6) 2
n
2
= −144
7) −6
m
2
= −414 8) 7
x
2
= −21
9)
m
2
+ 7 = 88 10) −5
x
2
= −500
11) −7
n
2
= −448 12) −2
k
2
= −162
13)
x
2
− 5 = 73 14) 16
n
2
= 49
-1-
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Worksheet by Kuta Software LLC
15)
n
2
− 5 = −4 16)
n
2
+ 8 = 80
17)
7
v
2
+ 1 = 29 18)
10
n
2
+ 2 = 292
19)
2
m
2
+ 10 = 210 20)
9
n
2
+ 10 = 91
21)
5
n
2
− 7 = 488 22)
8
n
2
− 6 = 306
23)
10
n
2
− 10 = 470 24)
8
n
2
− 4 = 532
25)
4
r
2
+ 1 = 325 26)
8
b
2
− 7 = 193
27)
2
k
2
− 2 = 144 28)
3 − 4
x
2
= −85
-2-
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 1 Name___________________________________
Period____Date________________
Solving Quadratic Equations with Square Roots
Solve each equation by taking square roots.
1)
k
2
= 76
{
8.717, −8.717
}
2)
k
2
= 16
{
4, −4
}
3)
x
2
= 21
{
4.582, −4.582
}
4)
a
2
= 4
{
2, −2
}
5)
x
2
+ 8 = 28
{
4.472, −4.472
}
6) 2
n
2
= −144
No solution.
7) −6
m
2
= −414
{
8.306, −8.306
}
8) 7
x
2
= −21
No solution.
9)
m
2
+ 7 = 88
{
9, −9
}
10) −5
x
2
= −500
{
10, −10
}
11) −7
n
2
= −448
{
8, −8
}
12) −2
k
2
= −162
{
9, −9
}
13)
x
2
− 5 = 73
{
8.831, −8.831
}
14) 16
n
2
= 49
{
1.75, −1.75
}
-1-
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Worksheet by Kuta Software LLC
15)
n
2
− 5 = −4
{
1, −1
}
16)
n
2
+ 8 = 80
{
8.485, −8.485
}
17)
7
v
2
+ 1 = 29
{
2, −2
}
18)
10
n
2
+ 2 = 292
{
5.385, −5.385
}
19)
2
m
2
+ 10 = 210
{
10, −10
}
20)
9
n
2
+ 10 = 91
{
3, −3
}
21)
5
n
2
− 7 = 488
{
9.949, −9.949
}
22)
8
n
2
− 6 = 306
{
6.244, −6.244
}
23)
10
n
2
− 10 = 470
{
6.928, −6.928
}
24)
8
n
2
− 4 = 532
{
8.185, −8.185
}
25)
4
r
2
+ 1 = 325
{
9, −9
}
26)
8
b
2
− 7 = 193
{
5, −5
}
27)
2
k
2
− 2 = 144
{
8.544, −8.544
}
28)
3 − 4
x
2
= −85
{
4.69, −4.69
}
-2-
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