Nth Root Calculator
Enter a number and a root degree to get the nth root instantly — the square root, cube root, or any higher root, all from the single formula x^(1/n).
Any root, one formula
Choose the degree — 2 for a square root, 3 for a cube root, or any higher number — and the calculator returns the nth root of your number right away.
Use non-negative numbers
The calculator works with numbers that are zero or positive, so the result is always a real number rather than a non-real even root.
What is an nth root?
The inverse of raising to a power
The nth root calculator finds the value that, when raised to the power n, gives back your original number. An nth root is simply the inverse of raising to a power: the square root undoes squaring, the cube root undoes cubing, and the fourth root undoes raising to the fourth. The degree n tells you which root to take — 2 for a square root, 3 for a cube root, and so on upward. Because every nth root can be written as the fractional exponent x^(1/n), one operation covers them all, which is exactly how this tool computes the answer from your number and the chosen degree.
Enter a number and a root degree to get the nth root instantly — the cube root of 27 is 3, because 3 × 3 × 3 = 27.
The nth root of a number is that number raised to the power one over the degree. Writing roots as fractional exponents means a single power operation handles every root, from the square root to any higher one.
ⁿ√x = x^(1/n)Take the cube root of 27 as a worked example. The degree is n = 3, so the exponent is 1/3, and the calculation is 27^(1/3). Since 3 × 3 × 3 = 27, the cube root is exactly 3. The same method gives the fourth root of 16 as 2 (because 2⁴ = 16) and the square root of 100 as 10 (because 10² = 100). Whenever the number is a perfect power, the root is a whole number; otherwise the calculator returns the decimal value rounded to six places, such as the square root of 2 ≈ 1.414214.
The formula is exact, but a couple of domain rules keep the result a real number.
Real numbers only — non-negative input, non-zero degree
This calculator works in the real-number domain, so the number must be zero or positive. An even root of a negative number — such as the square root of −4 — has no real value, and negative inputs are rejected rather than returning a complex result. The degree cannot be zero either, because the nth root is defined as x^(1/n) and dividing by zero is undefined. Stick to a non-negative number and a non-zero degree and the answer is always a real number.