Question 1

Which of the following equations can be solved most directly using the square root property?

Accepted Answer

$$x^2 - 9 = 0$

Question 2

Solve the equation $$x^2 = 25$ using the square root property. What is the solution set?

Accepted Answer

$$\{5, -5\}$$

Question 3

A ball is dropped from a height such that its height $$h (in $$meters) after $$t$$ seconds is given by $$h = 100 - 4.9t^2$. After how many seconds does the ball hit the ground? (Use the square root property.)

Accepted Answer

$$\sqrt{\dfrac{100}{4.9}}$$

Question 4

Which of the following is the correct application of the square root property to solve $$x^2 = 12$?

Accepted Answer

$$x = \pm \sqrt{12}$$

Question 5

Solve for $$x$$: $$x^2 + 7 = 0$.

Accepted Answer

$$x = \pm i\sqrt{7}$$

Question 6

A chemical reaction's rate is modeled by $$r^2 = 49$. What are the possible values for the rate r$?

Accepted Answer

$$\{7, -7\}$$

Question 7

If $$x^2 = -16$, what is the solution set?

Accepted Answer

$$\{4i, -4i\}$$

Question 8

Which step is necessary before applying the square root property to solve $$x^2 + 8 = 0$?

Accepted Answer

Subtract 8 from both sides to isolate $$x^2$$

Question 9

Solve for $$x$$: $$3x^2 = 27$

Accepted Answer

$$x = \pm 3$$

Question 10

A medical imaging device uses the equation $$d^2 = 144$ to determine the distance d$ (in mm) from a source. What are the possible values for d$?

Accepted Answer

$$\{12, -12\}$$

Question 11

Which of the following equations requires you to first isolate the squared term before applying the square root property?

Accepted Answer

$$2x^2 + 8 = 0$

Question 12

Solve for $$x$$: $$x^2 = 2$

Accepted Answer

$$x = \pm \sqrt{2}$$

Question 13

A projectile is launched vertically and its height $$h (in $$meters) after $$t$$ seconds is given by $$h = 20 - 5t^2$. When does it hit the ground?

Accepted Answer

$$t = \pm 2$$

Question 14

Solve for $$x$$: $$x^2 - 10 = 0$

Accepted Answer

$$x = \pm \sqrt{10}$$

Question 15

If $$x^2 = 0$, what is the solution set?

Accepted Answer

$$\{0\}$$

Question 16

Which of the following is a correct step in solving $$x^2 = -9$?

Accepted Answer

$$x = \pm 3i$$

Question 17

A satellite's distance from Earth is modeled by $$d^2 = 225$. What are the possible values for d$?

Accepted Answer

$$\{15, -15\}$$

Question 18

Solve for $$x$$: $$4x^2 = 64$

Accepted Answer

$$x = \pm 4$$

Question 19

Which of the following equations has only complex solutions?

Accepted Answer

$$x^2 + 1 = 0$

Question 20

Solve for $$x$$: $$x^2 = 49$

Accepted Answer

$$x = \pm 7$$

Solving Equations Using the Square Root Property

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