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
For access, consult one of our IM Certified Partners.
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
For access, consult one of our IM Certified Partners.
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
For access, consult one of our IM Certified Partners.
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
For access, consult one of our IM Certified Partners.
(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
For access, consult one of our IM Certified Partners.
(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
For access, consult one of our IM Certified Partners.
(From Unit 3, Lesson 7.)