Roots & Powers Calculator
Calculate square roots, cube roots, powers, and nth roots.
What are roots and powers and how does this calculator work?
This calculator handles four fundamental operations: square roots (√x), cube roots (∛x), powers (xʸ), and nth roots (ʸ√x). Select the operation, enter your number, and for powers or nth roots, add the exponent. The tool computes the exact result using JavaScript's Math functions, giving you precise answers for any real number input. It's useful for algebra, geometry, physics calculations, and everyday math problems involving squares, cubes, or general exponentiation.
How to use the Roots & Powers Calculator
Choose the operation from the dropdown — the input fields automatically adjust. For square or cube roots, just enter the number. For powers or nth roots, also enter the exponent/root degree. Click "Calculate" to see the result instantly. The calculator handles positive and negative numbers correctly (note: even roots of negative numbers are not real numbers).
Example calculations
√9 = 3. ∛27 = 3. 2⁵ = 32. ⁴√16 = 2. 5³ = 125. √2 ≈ 1.414. The calculator delivers precise results for all these operations in milliseconds.
Frequently Asked Questions
What happens if I try to take an even root of a negative number?
Even roots (square root, 4th root, etc.) of negative numbers are not real numbers. The calculator will show "Invalid input" because these results exist only in the complex number system. For real-number calculations, the radicand must be non-negative for even roots.
Can I calculate fractional exponents?
Yes, enter decimal values for the exponent (e.g. 0.5 for square root, 0.333 for cube root). The power function xʸ works with any real exponent. This is essentially the same as calculating nth roots — x^(1/n) equals the nth root of x.