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 \(\text-1 \boldcdot \text-1 = \text-1\).

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

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. \(\sqrt{\text-8}\)
Number line, scale -10 to 10, by 2’s.

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

Problem 3

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

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

Problem 4

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

A:

-5

B:

\(\frac15\)

C:

\(\frac13\)

D:

3

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted 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

Teachers with a valid work email address can click here to register or sign in for free access to Formatted 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:

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

Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(From Unit 3, Lesson 8.)