Nth Root Calculator

The 4th root of 81 is 3, because 3^4 = 3 x 3 x 3 x 3 = 81. You can also compute this as 81^(1/4) = 81^0.25 = 3.

Not in the real numbers. Even roots (2nd, 4th, 6th) of negative numbers have no real solution because no real number multiplied by itself an even number of times produces a negative result. However, odd roots of negatives are valid: the cube root of -27 = -3.

A square root finds what number times itself equals x (sqrt(9) = 3 because 3 x 3 = 9). A cube root finds what number times itself three times equals x (cbrt(27) = 3 because 3 x 3 x 3 = 27). Higher roots work the same way with more multiplications.

For perfect roots, factor the number: 81 = 3^4, so the 4th root is 3. For non-perfect roots, use estimation: the cube root of 50 is between 3 (3^3=27) and 4 (4^3=64), closer to 3.68. For precise values, use the formula x^(1/n) on any calculator.

Square roots appear in distance formulas (Pythagorean theorem), physics (kinetic energy), and statistics (standard deviation). Cube roots are used for finding dimensions of cubic volumes. In finance, nth roots calculate compound annual growth rate: CAGR = (final/initial)^(1/years) - 1.

Yes, the Nth Root Calculator is fully embeddable. Tap "Embed" above to configure appearance and copy the code. It is free to use, works on any platform (HTML, WordPress, CMS), and adjusts to any screen size automatically. Visit calculory.com/services/embed-calculators for the complete guide.