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. \(\sqrt[3]{x} = 3.75\)
    Y = cube root of x graphed on coordinate plane 
  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.)