The nth root of a number x is a value r such that r raised to the nth power equals x.

Can I find cube roots of negative numbers?

Yes. Odd-degree roots of negative numbers are real; for example, the cube root of -27 is -3.

Why is an even root of a negative number rejected?

No real number raised to an even power is negative. Such roots require complex numbers, which this real-root calculator does not display.

How are roots related to exponents?

The nth root of x can be written as x raised to the power 1/n.

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Root Calculator

Calculate square roots, cube roots, and any real nth root, including negative radicands for odd roots.

Maintained by CalculatorBuddy TeamUpdated September 29, 2026Editorial methodology

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Root

√81 = 9

Estimated result

Decimal Result: 9
Exponent Form: 81^(1/2)
Check: 9^2 = 81

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Root√81 = 9

Choose square root, cube root, or general nth root. Each result includes decimal and exponent forms plus a power check.

How to use this calculator

Choose the root degree before entering the radicand. Use an odd degree for negative numbers. Check the answer by raising it to the selected degree; a displayed decimal may differ slightly because of rounding.

Examples

Three exact roots

√81 = 9, ∛27 = 3, and the fifth root of 32 is 2 because 2⁵ = 32.

Formula

The nth root of x is x^(1/n). Square root uses n = 2 and cube root uses n = 3.

Root domain and precision

For real numbers, an even-index root of a negative radicand is undefined, while an odd-index root is negative. A principal root is one value; solving an equation such as x² = 9 has both +3 and −3. Irrational results are rounded for display, so use the radical form when an exact expression is required.

Frequently asked questions

What is an nth root?: The nth root of a number x is a value r such that r raised to the nth power equals x.
Can I find cube roots of negative numbers?: Yes. Odd-degree roots of negative numbers are real; for example, the cube root of -27 is -3.
Why is an even root of a negative number rejected?: No real number raised to an even power is negative. Such roots require complex numbers, which this real-root calculator does not display.
How are roots related to exponents?: The nth root of x can be written as x raised to the power 1/n.