Fourth Root Calculator — ⁴√x
Find the fourth root (⁴√x) of any non-negative number instantly. The fourth root is the inverse of raising a number to the fourth power — for example ⁴√256 = 4 because 4⁴ = 256.
Fourth root — the number that, raised to the power 4, equals x
- 1
Square root of x
√256 = 16The fourth root equals the square root taken twice: ⁴√x = √(√x). - 2
Square root of √x
√16 = 4
How does this calculator work?
The fourth root of x is x^(1/4) — equivalent to taking the square root twice. Enter any non-negative x and the calculator returns ⁴√x, verifies it by computing root⁴, and plots the y = x^(0.25) curve so you can see where your value lands.
Formula
How this is calculated
The fourth root of x is the number r such that r⁴ = x. Because the fourth power is always non-negative for real numbers, the fourth root only exists in the real number system for x ≥ 0. The calculator evaluates x^(0.25) directly, which is equivalent to taking the square root twice — first √x, then √(√x).
The verification row checks the result by raising it back to the power of 4; any tiny discrepancy is due to floating-point rounding and is not an error. For example, ⁴√625 = 5 (since 5⁴ = 625), ⁴√10000 = 10, and ⁴√2 ≈ 1.18921. Negative inputs are flagged because their fourth roots are complex (not real) numbers.
The curve shows y = x^(1/4) across the input range, with your value marked — useful for visualising how quickly the fourth root grows relative to x and how it flattens for large values.
Frequently asked questions
⁴√256 = 4, because 4 × 4 × 4 × 4 = 256. You can also verify it as √(√256) = √16 = 4.
Yes. ⁴√x = x^(1/4) = x^0.25. Roots are the inverse of powers, so the nth root equals x raised to 1/n.
Any real number raised to an even power is non-negative, so no real number can be the fourth root of a negative value. The fourth roots of negative numbers are complex (imaginary) and lie outside the scope of this calculator.
Also known as
TG we-Calculate Editorial Team. (2026). Fourth Root Calculator — ⁴√x [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/fourth-root-calculator
TG we-Calculate Editorial Team. "Fourth Root Calculator — ⁴√x." TG we-Calculate. 2026. https://we-calculate.com/calculator/fourth-root-calculator.
TG we-Calculate Editorial Team, "Fourth Root Calculator — ⁴√x," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/fourth-root-calculator
@misc{wecalculate_fourth_root_calculator, title = {Fourth Root Calculator — ⁴√x}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/fourth-root-calculator}}, year = {2026}, note = {TG we-Calculate} }
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