Root Approximator (Nth Root Calculator)

What an nth root is

If y = ⁿ√x, then yⁿ = x. Easy when x is a perfect power (√16 = 4, ∛27 = 3). Otherwise you iterate toward y.

• Newton–Raphson — usually fastest; good default
• Bisection — slower, but reliable if you bracket a root
• Babylonian — classic square-root iteration; easy to follow by hand

Method notes

Newton for √a averages the current guess with a/guess. Bisection halves an interval where the function changes sign. Pick precision (decimal places) and stop when successive guesses agree within that tolerance.

Odd roots of negatives are fine (∛(−8) = −2). Even roots of negatives need complex numbers — not covered here.

Frequently Asked Questions