# Lesson 8

Cubes and Cube Roots

- Let’s compare equations with cubes and cube roots.

### Problem 1

Select **all** equations for which -3 is a solution.

A:

\(x^2=9\)

B:

\(x^2=\text-9\)

C:

\(x^3=27\)

D:

\(x^3=\text-27\)

E:

\(\text-x^2 = 9\)

F:

\((\text- x)^2 = 9\)

### Problem 2

- Use the graph of \(y = \sqrt[3]{x}\) to estimate the solution(s) to the following equations.
- \(\sqrt[3]{x} = 2\)
- \(\sqrt[3]{x} = \text-4.5\)
- \(\sqrt[3]{x} = 3.75\)

- Use the meaning of cube roots to find exact solutions to all three equations.

### Problem 3

Which are the solutions to the equation \(x^3=\text-125\)?

A:

5

B:

-5

C:

both 5 and -5

D:

The equation has no solutions.

### Problem 4

Complete the table. Use powers of 16 in the top row. Use radicals or rational numbers in the second row.

\(16^{\text- \frac34}\) | \(16^{\text-\frac14}\) | |||

\(\frac{1}{16}\) | \(\frac14\) | 1 |

### Problem 5

Which are the solutions to the equation \(\sqrt{x}=\text-8\)?

A:

64 only

B:

-64 only

C:

64 and -64

D:

(From Unit 3, Lesson 6.)
This equation has no solutions.

### Problem 6

Find the solution(s) to each equation, or explain why there is no solution.

- \(x^2+6=55\)
- \(x^2+16=0\)
- \(x^2-3.25=21.75\)