What is a Root?
In mathematics, the root of a number x is another number y which, when raised to the power n, yields x. This is written as n√x = y.
Mathematical Relationship
n√x = y ⟺ yⁿ = x
Where n is the degree or index of the root, and x is the radicand.
Special Cases: Square and Cube Roots
The most common roots used in daily geometry and physics are the square root (degree 2) and the cube root (degree 3).
Square Root (√x)
Finding the side of a square given its area. For example, √9 = 3 because 3² = 9.
Cube Root (3√x)
Finding the edge of a cube given its volume. For example, 3√27 = 3 because 3³ = 27.
Common Perfect Roots Reference
| Number (x) | Square Root (√x) | Cube Root (3√x) | 4th Root (4√x) |
|---|---|---|---|
| 1 | 1 | 1 | 1 |
| 16 | 4 | 2.5198 | 2 |
| 64 | 8 | 4 | 2.8284 |
| 81 | 9 | 4.3267 | 3 |