Cube Roots
Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 5 of 43.
Cube roots simplify the same way, with perfect cubes in place of squares: 8, 27, 64, 125. The product rule holds here too, so for cbrt(24), split off 8, since 24 is 8 times 3:
cbrt(24) = cbrt(8) × cbrt(3) = 2cbrt(3)
A square factor is no use here. 4 divides 24, but cbrt(4) is not a whole number, so nothing comes out. Only a cube leaves a cube root, just as only a square leaves a square root.
Negatives come along too. Since -3 cubed is -27, cbrt(-27) is -3, and the minus sign can come out of a cube root whole. For cbrt(81): 81 is 27 times 3, so it is 3cbrt(3).
Challenge
Simplify cbrt(54). Type it as a product of two cube roots, the first of a perfect cube, then in simplified form. The board accepts a line only if it equals the one above.
Try it yourself
Write it in simplest radical form
Test yourselfThis 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 PowersPerfect Square FactorsThe Largest SquareLetters Under the RootCube RootsRecap: Simplifying Radicals7Powers and Roots Equations
Odd PowersEven PowersFractional PowersTwo Thirds PowerRecap: Power Equations