Can you find the square root of a negative number?

In the real number system, the square root of a negative number is undefined. However, in the complex number system, √(−1) is defined as the imaginary unit "i". So √(−9) = 3i. Our calculator handles real numbers and flags imaginary results.

What is the cube root of a negative number?

Unlike square roots, cube roots of negative numbers are perfectly real. For example, ∛(−27) = −3, because (−3)³ = −27. Multiplying three negative numbers yields a negative result, making odd-degree roots of negatives always real.

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📐 Math

Square & Cube Root Calculator

Calculate square roots, cube roots, and any nth root of any positive or negative number instantly.

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Number (x)

Root Type

Roots & Radicals — The Inverse of Powers

Square Root (√)

The square root of x is the non-negative number that, when multiplied by itself, equals x. √64 = 8 because 8² = 64. The square root is undefined for negative numbers in the real number system.

Cube Root (∛) — Negative Numbers Welcome

Unlike square roots, cube roots are defined for negative numbers. ∛−27 = −3 because (−3)³ = −27. This is because multiplying three negative numbers yields a negative result.

The nth Root Formula

Any nth root can be expressed as a fractional exponent: ⁿ√x = x^(1/n). This unifies root calculation with exponentiation, allowing consistent computation of any root degree through a single generalised formula.