MATH

Root Calculator

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Calculate principal real roots, including odd roots of negative numbers.

Your result

MATH

Enter your values and select calculate.

On this page How it works & practical examples

How to use the Root Calculator

Choose a positive whole-number degree and a radicand, the number under the root. The square root uses degree 2, the cube root degree 3 and so on. For a positive number and an even degree, the calculator returns the non-negative principal root. That is distinct from solving x^n = a, which may have more than one real or complex solution.

The calculation

For x ≥ 0: root = x^(1/n); for negative x and odd n: root = −|x|^(1/n)

Worked example

The cube root of 27 is 3 and the cube root of −27 is −3. The principal square root of 16 is 4.

Assumptions and limits

Negative radicands are supported only for odd degrees because even powers of real numbers cannot be negative. A degree of one returns the radicand. Floating-point approximation is used, so a root that is mathematically an exact integer may be rounded into that integer for display. Complex roots are outside this tool’s scope.

Common questions

Does √16 have two answers?

The principal square root is 4. Solving x² = 16 gives both 4 and −4, which is a different question.

Can I use a decimal root degree?

This tool restricts degree to a positive integer so the real-root convention remains clear.