# Lesson 10

A New Kind of Number

- Let’s invent a new number.

### Problem 1

Select **all **the true statements.

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

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

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

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

\(\sqrt{\text-1} = \text-1\) 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.

- \(\sqrt{4}\)
- \(\text- \sqrt{4}\)
- \(\sqrt{\text-4}\)
- \(\sqrt{8}\)
- \(\text- \sqrt{8}\)
- \(\sqrt{\text-8}\)

### Problem 3

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

### Problem 4

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

-5

\(\frac15\)

\(\frac13\)

3

### Problem 5

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

-19

19

21

The equation has no solutions.

### Problem 6

Select **all** equations for which -64 is a solution.

\(\sqrt{x} = 8\)

\(\sqrt{x} = \text-8\)

\(\sqrt[3]x = 4\)

\(\sqrt[3]x = \text-4\)

\(\text-\sqrt{x}=8\)

\(\sqrt{\text-x}=8\)