Root Calculator
Square root, cube root and nth root. Exact form or decimal; optional simplification.
Square Root Calculator
√
=
?
Example: √16 = 4
Cube Root Calculator
∛
=
?
Example: ∛27 = 3
nth Root Calculator
√
=
?
Example: ⁴√16 = 2
Roots in short
A root undoes a power: if yⁿ = x, then the nth root of x is y. Handy for finding a side from an area or volume.
- Square root: √x = y, if y² = x.
- Cube root: ∛x = y, if y³ = x.
- nth root: √[n]x = y, if yⁿ = x.
Useful Properties
- √(a × b) = √a × √b (if a, b ≥ 0).
- √(a²) = |a|.
- √[n](aⁿ) = a, if n is even and a ≥ 0.
- Roots can be written as fractional powers.
Calculation Methods
Simplify by splitting into square factors. E.g. √12 = √(4×3) = 2√3.
For nth roots, use known powers or approximate.
Examples
√12 = 2√3.
∛8 = 2.
⁴√81 = 3.
√72 = √(36×2) = 6√2.
Tips
- Negative number? With an even root exponent there is no real solution.
- How to simplify? Decompose into square numbers.
- For simplification and properties in plain language, try the main solver.