# 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

1. Use the graph of $$y = \sqrt[3]{x}$$ to estimate the solution(s) to the following equations.
1. $$\sqrt[3]{x} = 2$$
2. $$\sqrt[3]{x} = \text-4.5$$
3. $$\sqrt[3]{x} = 3.75$$
2. 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
(From Unit 3, Lesson 5.)

### Problem 5

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

A:

64 only

B:

-64 only

C:

64 and -64

D:

This equation has no solutions.

(From Unit 3, Lesson 6.)

### Problem 6

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

1. $$x^2+6=55$$
2. $$x^2+16=0$$
3. $$x^2-3.25=21.75$$
(From Unit 3, Lesson 7.)