Root Calculator
Work out square, cube or nth roots. Get an exact form or a decimal; simplify where possible.
Square Root Calculator
√
=
?
Example: √16 = 4
Cube Root Calculator
∛
=
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Example: ∛27 = 3
nth Root Calculator
√
=
?
Example: ⁴√16 = 2
Roots in short
A root is the reverse of a power: if yⁿ = x, then the nth root of x is y. Useful when you know an area or volume and want a length.
- 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 writing the number as a product of square factors. E.g. √18 = √(9×2) = 3√2.
For nth roots, use known perfect nth powers or a decimal approximation.
Examples
√18 = 3√2.
∛27 = 3.
⁵√32 = 2.
√50 = √(25×2) = 5√2.
Tips
- Negative input? For an even root (e.g. square root) there is no real number result.
- How to simplify? Split the number into square factors (4, 9, 16, …).
- For simplification and properties explained in plain language, use the main solver.