Root Calculator

Find the principal real nth root — square root, cube root or another degree — including the cube root of a negative, but not the square root of one.

How to use

Enter the number under the radical.
Enter the degree: 2 for square root, 3 for cube root, 4 for fourth root.
Read the principal real root. √9 is 3, not −3, even though (−3)² is also 9.
Use the exponent calculator if you already think in 9^(1/2) rather than a radical.

How it works

The nth root of x is a number r with r^n = x. Degree 2 is the familiar square root: √9 = 3. Degree 3 is the cube root: ³√27 = 3 and ³√−8 = −2. Even degrees of negatives have no real answer; the page stays blank instead of inventing a complex number.

The principal square root is the non-negative one. Quadratic equations still have two roots; this tool is not the quadratic solver.

A 0th root is undefined. Degree 1 is the number itself. Non-integer degrees are treated as real powers x^(1/n) when that is real.

Floating-point pow() returns NaN for many negative bases. This page applies a sign correction for odd integer degrees so ³√−8 is −2.

Overflow and domain errors are withheld. If you need every complex nth root, you need a CAS, not this page. Powers such as 2^8 belong on the exponent calculator.

√2 is irrational; the display is a rounded float, not a proof. Nested radicals such as √(√16) are two steps (4, then 2), not a single degree-4 button unless you set degree 4 on 16. Area-to-side work is a square root of the area only for a square, not for a rectangle.

Formula

ⁿ√x = x^(1/n)
√9 = 3
³√−8 = −2

Worked examples

Square root
9 with degree 2 → 3
Cube root of a negative
−8 with degree 3 → −2

Roots that should stay exact

Expression	Result
√9	3
√16	4
⁴√16	2
³√27	3
³√−8	−2
√0	0

Useful notes

Principal real root only — √9 is 3, not ±3.
Even roots of negatives are rejected.
0th root is undefined.

FAQ

How do I find a square root?: Use degree 2. The square root of 9 is 3 because 3×3 = 9.
Can I take an even root of a negative number?: Not on the real line. There is no real number whose square is −9. The tool reports no result instead of NaN.
Is the cube root of a negative allowed?: Yes. (−2)×(−2)×(−2) = −8, so ³√−8 = −2.
What is the fourth root of 16?: 2, because 2^4 = 16. −2 is also a real fourth power, but the principal root is 2.
Why isn’t √9 shown as ±3?: The radical symbol means the principal (non-negative) root. The ± appears when you solve x² = 9.

Related tools

See all Math tools.