The cube root of 27 is 3, because 3 × 3 × 3 = 27.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Where the name comes from
A cube of volume 27 has edges of 3. The cube root is that edge length.
Negatives are allowed here
The cube root of −8 is −2, because (−2)³ = −8. A square root of a negative has no such answer.
Telling them apart
A square root asks for two equal factors; a cube root asks for three.
The side length of a cube
∛27 = 3 because 3 × 3 × 3 = 27. Just as a square root gives the side of a square with a given area, a cube root gives the side of a cube with a given volume. The names describe the geometry.
Cube roots of negatives exist
∛(−8) = −2, because (−2)³ = −8. Unlike square roots, cube roots of negative numbers are perfectly ordinary, since an odd number of negative factors gives a negative product. This asymmetry surprises people.
Only one cube root
Every real number has exactly one real cube root, positive or negative. There is no ± to worry about, which makes solving x³ = 27 simpler than solving x² = 9.
Where cube roots are needed
Finding the edge of a cubical tank from its volume, or the scale factor between two similar solids from their volumes. Any time a quantity depends on three dimensions, undoing it needs a cube root.
Step 2: Try It Yourself
Tap and try it out.
- Cubes in one layer3 × 3 = 9
- Layers3
- 3 × 3 × 327 cubic units
Counting every cube gives 27, and so does 3 × 3 × 3. The formula is a shortcut for the count.
Step 3: Watch an Example
One step at a time.
Watch Ana Find an Edge
A cube has a volume of 64 cubic centimetres.
- Step 1
She needs the number that multiplies by itself three times to give 64.
Step 4: Your Turn
Practice makes it stick.
The Cube
Problem 1 of 2
A cube has volume 125. What is its edge length?
The Negative
Problem 2 of 2
What is the cube root of −27?
Three Equal Factors
1 of 4
Cube root of 8?
2 of 4
Cube root of 1000?
3 of 4
Square root of 49?
4 of 4
Cube root of −64?
Step 5: Quick Check
Show what you know.
Question 1 of 1
Cube root of 216?
What You Learned
- A cube root asks which number multiplied by itself three times gives the value.
- It is the edge length of a cube with that volume.
- Cube roots of negative numbers exist; square roots of negatives do not.