Root Calculator
Use our root calculators for square root, cube root and nth root – fast and clear.
Square Root Calculator
√
=
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Example: √16 = 4
Cube Root Calculator
∛
=
?
Example: ∛27 = 3
nth Root Calculator
√
=
?
Example: ⁴√16 = 2
Quick Guide to Roots
The root is the inverse of a power: if yⁿ = x, then the nth root of x equals y. Useful e.g. to determine an edge length or a value 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
To simplify a root, decompose the number into square numbers. Example: √18 = √(9 × 2) = 3√2.
For the nth root, try powers or use an approximation.
Examples
√18 = 3√2.
∛27 = 3.
⁴√16 = 2.
√(50) = √(25×2) = 5√2.
FAQ
- Negative number? With an even root exponent there is no real solution.
- How to simplify? Decompose into square numbers.
- Need explanations? The Math AI assistant can explain in detail.