# Lesson 10

A New Kind of Number

### Problem 1

Select all the true statements.

A:

$$\sqrt{\text-1}$$ is an imaginary number.

B:

There are no real numbers that satisfy the equation $$x=\sqrt{\text-1}$$.

C:

Because $$\sqrt{\text-1}$$ is imaginary, no one does math with it.

D:

The equation $$x^2 = \text-1$$ has real solutions.

E:

$$\sqrt{\text-1} = \text-1$$ because $$\text-1 \boldcdot \text-1 = \text-1$$.

### Problem 2

Plot each number on the real number line, or explain why the number is not on the real number line.

1. $$\sqrt{4}$$
2. $$\text- \sqrt{4}$$
3. $$\sqrt{\text-4}$$
4. $$\sqrt{8}$$
5. $$\text- \sqrt{8}$$
6. $$\sqrt{\text-8}$$

### Problem 3

Explain why $$(x-4)^2=\text-9$$ has no real solutions.

### Problem 4

Which value is closest to $$10^{\text- \frac12}$$?

A:

-5

B:

$$\frac15$$

C:

$$\frac13$$

D:

3

### Solution

(From Unit 3, Lesson 5.)

### Problem 5

Which is a solution to the equation $$\sqrt{6-x}+5=10$$?

A:

-19

B:

19

C:

21

D:

The equation has no solutions.

### Solution

(From Unit 3, Lesson 7.)

### Problem 6

Select all equations for which -64 is a solution.

A:

$$\sqrt{x} = 8$$

B:

$$\sqrt{x} = \text-8$$

C:

$$\sqrt[3]x = 4$$

D:

$$\sqrt[3]x = \text-4$$

E:

$$\text-\sqrt{x}=8$$

F:

$$\sqrt{\text-x}=8$$