Unit 4, Lesson 8

Cubes and Cube Roots

Algebra 2

Practice

Problem 1

Select all equations for which -3 is a solution.

\(x^2=9\)
\(x^2=\text-9\)
\(x^3=27\)
\(x^3=\text-27\)
\(\text-x^2 = 9\)

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

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Problem 2

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. \(\sqrt[3]{x} = 3.75\)
Use the meaning of cube roots to find exact solutions to all three equations.

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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.

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Problem 4

ForLesson 5: Negative Rational Exponents

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

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Problem 5

ForLesson 6: Squares and Square Roots

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

64 only
-64 only
64 and -64
This equation has no solutions.

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Problem 6

ForLesson 7: Inequivalent Equations?

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

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

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Cubes and Cube Roots

Practice

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Lesson 8 Resources