Quiz about Solving Equations by Taking the Square Root

Question 1

Solve by taking the square root:
x² = 49

Accepted Answer

-7, 7

Answer

-7

Answer

7

Answer

49

Question 2

Solve by taking the square root:
4x² = 100

Accepted Answer

-5, 5

Answer

-10, 10

Answer

-25, 25

Answer

5

Question 3

x² -4 = 77

Accepted Answer

9, -9

Answer

9

Answer

-9

Answer

No Real Solutions

Question 4

Solve by taking square roots:
3 + 9r² = 12

Accepted Answer

r = 1, r = -1

Answer

r = 0

Answer

no solution

Answer

r = 3, r = -3

Question 5

Solve using square roots.

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 6

Solve.
2(2x - 4)² = 32

Accepted Answer

x = 0, 4

Answer

x = 4

Answer

x = 10

Answer

x = -2

Question 7

If a student correctly finds x = 3i is one solution to a quadratic equation, what is the other?

Accepted Answer

- 3i

Answer

3

Answer

- 3

Answer

can not be determined

Question 8

Solve the quadratic equation by taking the square roots. Allow for imaginary solutions.

$$10x^2-15\ =\ 5x^2-40$$

Accepted Answer

$$x\ =\ \pm i\sqrt{5}$$

Answer

$$x\ =\ \pm5i$$

Answer

$$x\ =\ \pm25$$

Answer

$$x\ =\ \pm\frac{5}{25}i$$

Question 9

Solve the quadratic equation by taking the square roots. Allow for imaginary solutions.

$$x^2+9\ =\ 3$$

Accepted Answer

$$x\ =\ \pm i\sqrt{6}$$

Answer

$$x\ =\ \pm3$$

Answer

$$x\ =\ \pm9$$

Answer

$$x\ =\ \pm\sqrt{6}$$

Question 10

Solve by taking square roots.
$$x^2=12$$

Hint: Remember to simplify your answer!

Accepted Answer

$$\left\{\pm\ 2\sqrt{3}\right\}$$

Answer

$$\left\{\sqrt{12}\right\}$$

Answer

$$\left\{144\right\}$$

Answer

$$\left\{6\right\}$$

Question 11

Solve by taking square roots.
$$\left(x-14\right)^2=36$$

Accepted Answer

$$\left\{8,\ 20\right\}$$

Answer

$$\left\{20\right\}$$

Answer

$$\left\{-8,\ -20\right\}$$

Answer

$$\left\{-22\right\}$$

Question 12

Find the x-intercept(s) by taking square roots.
$$\left(x-1\right)^2=6$$

Accepted Answer

$$\left\{1\pm\sqrt{6}\right\}$$

Answer

$$\left\{\pm\sqrt{6}-1\right\}$$

Answer

$$\left\{37\right\}$$

Answer

$$\left\{1\pm\sqrt{3}\right\}$$

Question 13

Solve by taking square roots.
$$\left(2x+1\right)^2=4$$

Accepted Answer

$$\left\{-\frac{3}{2},\ \frac{1}{2}\right\}$$

Answer

$$\left\{\pm\ 2\right\}$$

Answer

$$\left\{\pm\ \frac{1}{2}\right\}$$

Answer

$$\left\{-\frac{1}{2},\ \frac{3}{2}\right\}$$

Question 14

Find the zero(s) by taking square roots.
$$\left(3x+8\right)^2=36$$

Accepted Answer

$$\left\{-\frac{14}{3},\ -\frac{2}{3}\right\}$$

Answer

$$\left\{-\frac{2}{3},\ 0\right\}$$

Answer

$$\left\{\frac{2}{3},\ \frac{14}{3}\right\}$$

Answer

$$\left\{\frac{28}{3}\right\}$$

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