# Lesson 8

Cubes and Cube Roots

### Problem 1

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

\(x^2=9\)

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

\(x^3=27\)

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

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

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

### Solution

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### 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.

### Solution

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### Problem 3

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

5

-5

both 5 and -5

The equation has no solutions.

### Solution

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### 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 |

### Solution

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(From Unit 3, Lesson 5.)### Problem 5

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

64 only

-64 only

64 and -64

This equation has no solutions.

### Solution

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(From Unit 3, Lesson 6.)### Problem 6

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

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

### Solution

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(From Unit 3, Lesson 7.)