arithmetic
What is a Cube Root?
⚡ THE DEFINITION
The cube root of a number is the value that, when multiplied by itself three times, gives the original number.
∛x = y ⇔ y³ = x← THE DEFINITION
The Concept of Cubing
To understand cube roots, we first look at cubing. When we cube a number, we multiply it by itself three times. For example, 3 cubed is 3 × 3 × 3 = 27.
Parts of the Cube Root Symbol
1
Radical Sign
The ∛ symbol used to indicate a root.
2
Index
The small 3 in the radical, which tells us it is a cube root (not a square root).
3
Radicand
The number inside the radical sign.
Perfect Cubes to Remember
∛1 = 11 × 1 × 1 = 1
∛8 = 22 × 2 × 2 = 8
∛27 = 33 × 3 × 3 = 27
∛64 = 44 × 4 × 4 = 64
∛125 = 55 × 5 × 5 = 125
💡Important Rules
- Negative numbers HAVE real cube roots (unlike square roots!). For example, ∛-8 = -2.
- A perfect cube is an integer whose cube root is also an integer.
- Use estimation for cube roots that aren't perfect cubes (e.g., ∛30 is between 3 and 4).