Cube Roots

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 6 of 40.

A cube root undoes a cube. $\sqrt[3]{8} = 2$ , because ${2}^{3} = 8$ . It also works for negative numbers: $\sqrt[3]{-8} = -2$ , because $\left(-2\right)^3 = -8$ .

You simplify cube roots like square roots, but you take out perfect cubes: 8, 27, 64 and 125.

$\sqrt[3]{24} = \sqrt[3]{8} \cdot \sqrt[3]{3} = 2\sqrt[3]{3}$

A perfect square, like 4, does not help inside a cube root.

Challenge

Simplify $\sqrt[3]{-54}$ . First write it as two cube roots multiplied, with a perfect cube in the first. Then write it in simplest form.

Try it yourself

\sqrt[3]{-54}

Write it in simplest radical form

All lessons in Radicals & Rational Exponents

1Simplest Form

Perfect Square Factors Like Radicals Simplify First Recap: Adding Radicals

4Rationalizing

One Root Below A Number and a Root The Conjugate Below Recap: Rationalizing

7Powers and Roots Equations

Odd Powers Even Powers Fractional Powers Two Thirds Power Recap: Power Equations

2Letters and Cube Roots

Letters Under the RootCube RootsRecap: Simplifying Radicals

5Rational Exponents

One Over n m Over n Negative Exponents Exponent Rules Still Work Recap: Rational Exponents

8Radical Functions

Domain of a Root Evaluating Inverse of a Square Recap: Radical Functions

3Multiplying Radicals

Root Times Root Distributing a Root Two Brackets Conjugate Pairs Recap: Multiplying Radicals

6Radical Equations

Square Both Sides Isolate the Root First A False Answer Cube Root Equations Recap: Radical Equations

9Final Challenges

Final: Simplify and Add Final: Clear the Root Final: The Exponent Final: Check It Final: The Falling Ball