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Solving Quadratic Equations (using Square Roots) Worksheet

Solving Quadratic Equations (using Square Roots) Worksheet
  • Page 1
 1.  
The area of a circular garden is given by the equation, A = 3.14r2, where A is the area of the garden in square ft and r is the radius of the garden in ft. What is the radius of the garden, if its area is 7850 sqaure ft?
a.
55 ft
b.
25 ft
c.
50 ft
d.
None of the above


Solution:

Area of a circular garden, A = 3.14r2

7850 = 3.14r2
[Substitute 7850 for A.]

78503.14 = r2
[Divide each side by 3.14.]

2500 = r2
[Simplify.]

r = √2500 = ±50
[Take square root on both sides.]

Radius of the garden cannot be negative. So, r = 50 ft.


Correct answer : (3)
 2.  
A circular dining table has an area of 78.50 square ft. What is the radius of the table, if its area is modeled by the equation A = 3.14r2, where A is its area in square ft and r is its radius in ft?
a.
4 ft
b.
5 ft
c.
6 ft
d.
None of the above


Solution:

A = 3.14r2
[Original equation.]

78.50 = 3.14r2
[Substitute 78.50 for A.]

78.50 / 3.14 = 3.14 / 3.14r2
[Dividing each side by 3.14.]

25 = r2
[Simplify.]

r = √25 = ±5
[Take square root on both sides.]

So, radius of the table, r = +5 ft
[Radius of table cannot be negative.]


Correct answer : (2)
 3.  
Solve 5z2 + 20 = 415 and round the result to its nearest tenth.
a.
± 11.6
b.
± 11.2
c.
± 8.9
d.
None of the above


Solution:

5z2 + 20 = 415
[Original equation.]

5z2 = 395
[Subtract 20 from each side.]

z2 = 79
[Divide with 5 on both sides.]

z = ± 8.9
[Take square root on both sides and round to the nearest tenth.]


Correct answer : (3)
 4.  
What integral values of x satisfy the equation x2 = 64?
a.
64
b.
-8
c.
8, -8
d.
9, -9


Solution:

x2 = 64
[Original equation.]

x = ±√64
[Take square root on both sides.]

x = ±8
[82 = 64 and (-8)2 = 64.]

The values of x satisfying the equation are 8 and -8.


Correct answer : (3)
 5.  
Solve the equation p2 = 7 and express the solutions as radical expressions.
a.
-√7
b.
+√7
c.
+√7,-√7
d.
√7,√7


Solution:

p2 = 7
[Original equation.]

p = ±√7
[Take square root on both sides.]

p = √7 and p = -√7
[Simplify.]

The solutions of the equation in the form of radical expressions are -√7 and +√7.


Correct answer : (3)
 6.  
Express the solutions of the equation m2 - 15 = 21, as integers.
a.
- 6
b.
+ 6
c.
+6, -6
d.
6, 6


Solution:

m2 - 15 = 21
[Original equation.]

m2 = 36
[Add 15 to each side.]

m = ±√36
[Evaluate square root on both sides.]

m = ±6
[Simplify.]

The solutions of the equation in the form of integers are +6 and -6.


Correct answer : (3)
 7.  
Express the solutions of the equation 2n2 - 14 = 10, in the form of radical expressions.
a.
+√12
b.
+√12, -√12
c.
√12, √12
d.
-√12


Solution:

2n2 - 14 = 10
[Original equation.]

2n2 - 14 + 14 = 10 +14
[Add 14 to each side.]

2n2 = 24
[Simplify.]

n2 = 12
[Divide each side by 2.]

n = ±√12
[Take square root on both sides.]

The solutions of the equation in the form of radical expressions are +√12 and -√12.


Correct answer : (2)
 8.  
Solve the equation (k2)/3 = 0.
a.
k = 1
b.
k = 0,1
c.
k = 0,0
d.
k = 0


Solution:

(k2)/3 = 0
[Original equation.]

(k2) = 0
[Multiply each side with 3.]

k = 0
[Evaluate square root on both sides.]


Correct answer : (4)
 9.  
Solve the equation 3c2 = - 9.
a.
- 3
b.
+3
c.
No solution
d.
±3


Solution:

3c2 = - 9
[Original equation.]

c2 = - 3
[Divide each side by 3.]

The square of a real number is never negative.

So, the equation 3c2 = - 9, has no real solution.


Correct answer : (3)
 10.  
Solve the equation 4w2 - 16 = 0.
a.
3, - 3
b.
- 2
c.
4, - 4
d.
2 , - 2


Solution:

4w 2 - 16 = 0
[Original equation.]

4w 2 = 16
[Add 16 to each side.]

w 2 = 4
[Divide each side by 4.]

w = ±√4
[Evaluate square root on both sides.]

w = ±2
[Simplify.]


Correct answer : (4)

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