﻿ Solving Quadratic Equations (using Square Roots) Worksheet | Problems & Solutions

# Solving Quadratic Equations (using Square Roots) Worksheet

Solving Quadratic Equations (using Square Roots) Worksheet
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1.
The area of a circular garden is given by the equation, $A$ = 3.14$r$2, 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.

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 $A$ = 3.14$r$2, 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.]

3.
Solve 5$z$2 + 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.]

4.
What integral values of $x$ satisfy the equation $x$2 = 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.

5.
Solve the equation $p$2 = 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.

6.
Express the solutions of the equation $m$2 - 15 = 21, as integers.
 a. - 6 b. + 6 c. +6, -6 d. 6, 6

#### Solution:

m2 - 15 = 21
[Original equation.]

m2 = 36

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.

7.
Express the solutions of the equation 2$n$2 - 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

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.

8.
Solve the equation ($k$2)/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.]

9.
Solve the equation 3$c$2 = - 9.
 a. - 3 b. +3 c. No solution d. Ã‚Â±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.

10.
Solve the equation 4$w$2 - 16 = 0.
 a. 3, - 3 b. - 2 c. 4, - 4 d. 2 , - 2

#### Solution:

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

4w 2 = 16

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

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

w = ±2
[Simplify.]