Solving Quadratic Equations (using Square Roots) Worksheet

**Page 1**

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 |

7850 = 3.14

[Substitute 7850 for

[Divide each side by 3.14.]

2500 =

[Simplify.]

[Take square root on both sides.]

Radius of the garden cannot be negative. So,

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 $A$ = 3.14$r$^{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 |

[Original equation.]

78.50 = 3.14

[Substitute 78.50 for

[Dividing each side by 3.14.]

25 =

[Simplify.]

[Take square root on both sides.]

So, radius of the table,

[Radius of table cannot be negative.]

Correct answer : (2)

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 |

[Original equation.]

5

[Subtract 20 from each side.]

[Divide with 5 on both sides.]

[Take square root on both sides and round to the nearest tenth.]

Correct answer : (3)

4.

What integral values of $x$ satisfy the equation $x$^{2} = 64?

a. | 64 | ||

b. | -8 | ||

c. | 8, -8 | ||

d. | 9, -9 |

[Original equation.]

[Take square root on both sides.]

[8

The values of

Correct answer : (3)

5.

Solve the equation $p$^{2} = 7 and express the solutions as radical expressions.

a. | -√7 | ||

b. | +√7 | ||

c. | +√7,-√7 | ||

d. | √7,√7 |

[Original equation.]

[Take square root on both sides.]

[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 $m$^{2} - 15 = 21, as integers.

a. | - 6 | ||

b. | + 6 | ||

c. | +6, -6 | ||

d. | 6, 6 |

[Original equation.]

[Add 15 to each side.]

[Evaluate square root on both sides.]

[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 2$n$^{2} - 14 = 10, in the form of radical expressions.

a. | +√12 | ||

b. | +√12, -√12 | ||

c. | √12, √12 | ||

d. | -√12 |

[Original equation.]

2

[Add 14 to each side.]

2

[Simplify.]

[Divide each side by 2.]

[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 ($k$^{2})/3 = 0.

a. | $k$ = 1 | ||

b. | $k$ = 0,1 | ||

c. | $k$ = 0,0 | ||

d. | $k$ = 0 |

[Original equation.]

(

[Multiply each side with 3.]

[Evaluate square root on both sides.]

Correct answer : (4)

9.

Solve the equation 3$c$^{2} = - 9.

a. | - 3 | ||

b. | +3 | ||

c. | No solution | ||

d. | Ã‚Â±3 |

[Original equation.]

[Divide each side by 3.]

The square of a real number is never negative.

So, the equation 3

Correct answer : (3)

10.

Solve the equation 4$w$^{2} - 16 = 0.

a. | 3, - 3 | ||

b. | - 2 | ||

c. | 4, - 4 | ||

d. | 2 , - 2 |

[Original equation.]

4

[Add 16 to each side.]

[Divide each side by 4.]

[Evaluate square root on both sides.]

[Simplify.]

Correct answer : (4)