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Cube Root Equations

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 28 of 43.

Cubing undoes a cube root: (cbrt(u))^3 is u. Take cbrt(x + 1) = -3. Cube both sides: x + 1 = -27, so x is -28. Check: cbrt(-27) is -3, because (-3)^3 = -27.

Notice the right side was negative, and that was fine. The cube root of a negative number is negative, so cbrt(u) = -3 is a sensible equation, unlike √(u) = -3.

Cubing never creates a false answer, because it keeps signs: 5 cubed is 125 and -5 cubed is -125. Two different real numbers never have the same cube, so if the cubes match, the numbers match. That is why no check is needed after cubing.

Challenge

Solve cbrt(x - 2) = 3.

Try it yourself

cbrt(x - 2) = 3

Solve for x

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Radicals & Rational Exponents

1Simplifying Radicals

Roots and Powers Perfect Square Factors The Largest Square Letters Under the Root Cube Roots Recap: Simplifying 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

2Adding & Subtracting Radicals

Like Radicals Simplify First Subtracting Recap: Adding 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 AnswerCube Root EquationsRecap: Radical Equations

9Final Challenges

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