Root Calculator
Calculate any nth root — square root, cube root, fourth root and higher — of any positive real number.
How to use the Root Calculator
- Enter your inputs into the Root Calculator above.
- Results update instantly as you type — no submit button needed.
- Adjust any value to see how the result changes in real time.
The root definition
ⁿ√x = x^(1/n) · · · because (x^(1/n))^n = x
The nth root of x is the value that, raised to the nth power, gives x. Square root is the 2nd root; cube root is the 3rd; nth root in general is the 1/n power.
Worked example
√144 = 12 (because 12² = 144). ∛125 = 5 (because 5³ = 125). The 4th root of 81 = 3 (because 3⁴ = 81). The 5th root of 32 = 2 (because 2⁵ = 32).
Frequently asked questions
Can I take roots of negative numbers?
Yes for odd roots (∛−8 = −2). No for even roots over real numbers (√−4 is not a real number — it's an imaginary number, 2i in complex math).
What is ⁿ√0?
Always 0, for any n ≥ 1 — because 0 raised to any positive power equals 0.
How do I simplify radicals?
Factor out perfect powers. √72 = √(36 × 2) = 6√2. ∛54 = ∛(27 × 2) = 3∛2.