Root Calculator
Take the square root, cube root or any nth root of a number, with a built-in check of the answer.
How it works
ⁿ√x = x^(1/n)
The nth root undoes the nth power. Odd roots work for negative numbers (the cube root of −27 is −3, since a negative times itself three times stays negative), but even roots of negatives have no real answer — no real number squared comes out negative. Computationally, the root is the fractional power x^(1/n).
Worked example
The cube root of 27 is 3, because 3 × 3 × 3 = 27. The 5th root of 32 is 2, and the square root of 2 is about 1.41421356 — an irrational number whose decimals never repeat.
Frequently asked questions
Why can’t I take the square root of a negative number?
Any real number times itself is positive or zero, so nothing real squares to −9. Mathematicians handle it with the imaginary unit i, where √−9 = 3i, but that leaves the real number line.
Doesn’t every positive number have two square roots?
Yes — 9 has roots 3 and −3. The radical symbol and this calculator return the principal (positive) root by convention; add the ± yourself when solving equations.
How were roots computed before calculators?
By iteration. Heron’s method for square roots averages a guess g with x ÷ g and repeats — starting at 1.5 for √2, two rounds already give 1.4142.
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This calculator is for educational purposes. Double-check important results before acting on them.