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Root Calculator

Find square, cube and nth roots, and simplify radicals such as √72 = 6√2.

Result

Enter your values and select Calculate to see the result.

Runs in your browser — nothing you enter is sent to a server.

How the Root Calculator works

The nth root of x is the number that, multiplied by itself n times, gives x. Choose square, cube or a higher root. The calculator says whether the root is exact, and for whole numbers it also gives the simplified radical form by taking out perfect powers.

Formula

ⁿ√x = x1/n

Odd roots of negative numbers are negative; even roots of negative numbers aren't real.

Examples

Exact roots

∛27 = 3 and the 5th root of −32 is −2.

Simplified radicals

√72 ≈ 8.485281 = 6√2, because 72 = 36 × 2; ∛24 = 2∛3.

Frequently asked questions

Why simplify a radical?

Schoolwork and exact answers often want 6√2 rather than a rounded decimal.

Is √x the same as x to the power 0.5?

Yes; the Exponent Calculator gives the same result.

What about square roots of negative numbers?

They are imaginary numbers (√−4 = 2i), which this calculator doesn't cover.

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