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Cubes and Cube Roots

Cubes and Cube Roots · Class VIII

Slide n for its cube and N for its cube root.

3
type a value
-1010
125
type a value
-10001000
Live values
  • n^327
  • cbrt(N)5
  • Perfect cube? (1 yes)1
xy
  • x^3

Formulas in this lab

  • n^3
    n3n^{3}
  • cbrt(N)
    N3\sqrt[3]{N}
  • Perfect cube? (1 yes)
    [N3∈Z][\sqrt[3]{N} \in \mathbb{Z}]
Tip: Negative numbers do have real cube roots, unlike square roots.

Frequently asked questions

▶What is a cube root?

The cube root of N is the number that, cubed, gives N. So cbrt(125) = 5 because 5 * 5 * 5 = 125. Unlike square roots, cube roots can be negative: cbrt(-27) = -3 because -3 * -3 * -3 = -27.

▶How do I use the cubes and cube roots lab?

Slide n between -10 and 10 to see n^3, and slide N between -1000 and 1000 to see cbrt(N). Try n = 4 to see 64, and N = 216 to see 6. Negative values work for both sliders, unlike with square roots.

▶Where do cubes show up in real life?

Storage tanks, water cubes, sugar cubes and dice are all real cubic shapes. A water tank of side 2 m holds 2^3 = 8 cubic metres or 8000 litres. The lab gives quick volume checks for any cube-side from 0 to 10.

▶Cubes vs squares: how are they different?

A square uses two equal factors (n*n) and stays positive. A cube uses three equal factors (n*n*n) and keeps the sign of n. So (-4)^2 = 16 but (-4)^3 = -64. The lab makes the contrast clear: slide n to negative and watch the square stay positive while the cube flips negative.