Square Root / Nth Root Calculator
Calculate the square root, cube root, or any nth root of a number. Handles negative numbers for odd roots (where defined) and shows results in multiple forms.
Inputs
n=2 for square root, n=3 for cube root, etc.
nth root
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Square root (n=2)
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Cube root (n=3)
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Check: result^n
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About Square Root / Nth Root Calculator
Why no even root of negative?
In real numbers, x² ≥ 0 always, so no real x squares to a negative. The complex solution exists (using i = √−1) but this calculator stays in real numbers.
Odd roots of negatives
These do exist: ∛(−8) = −2 because (−2)³ = −8. The cube of a negative is negative, so cube roots preserve sign.
Connection to exponents
The nth root of x is x^(1/n). All root calculations here use this identity via JavaScript’s Math.pow.