How this calculator works
A fourth power multiplies a number by itself four times. Its principal real fourth root is always non-negative. For a whole-number input up to one billion, prime exponents are split into groups of four: every complete group leaves the radical. Larger integers and decimals retain an unsimplified radical label alongside their approximate root. The common-power table helps check perfect powers. Solving x⁴=a is a different question from evaluating ⁴√a, because a positive a has both positive and negative real equation solutions.
Formula
⁴√a = sqrt(sqrt(a)) for a ≥ 0. If a = c⁴d with c ≥ 0, then ⁴√a = c × ⁴√d. For a > 0, x⁴=a has x = ±⁴√a.
Worked example
162 = 81 × 2 = 3⁴ × 2, so ⁴√162 = 3 × ⁴√2 ≈ 3.567621345. For 81 the principal root is 3, while the equation x⁴=81 has the two real solutions -3 and 3.
Advertisement
Frequently asked questions
Why does a negative input fail?
Every real number raised to the fourth power is non-negative. A negative input has complex fourth roots, which this real-number tool does not calculate.
Does the fourth root mean dividing by four?
No. The fourth root of 16 is 2 because 2⁴=16. Dividing 16 by four gives 4, a different operation.
Can I enter a decimal?
Yes. For example ⁴√0.0625=0.5. Exact factor extraction is restricted to the stated whole-number range.