This fourth root calculator instantly computes the fourth root of any positive number. Enter a value and the result updates in real time.
Fourth root calculator
What is a fourth root?
The fourth root of a number is the value that, when multiplied by itself four times, equals the original number. Written as ∜x or x^(1/4).
For example: ∜81 = 3, because 3 × 3 × 3 × 3 = 81.
Like square roots, fourth roots only work for non-negative numbers in the real number system. The fourth root of a negative number is undefined (it would require imaginary numbers).
Perfect fourth powers
A perfect fourth power is a number whose fourth root is a whole number. The calculator shows a "Perfect Root" badge when you enter one. The first ten perfect fourth powers:
- 1 (1⁴)
- 16 (2⁴)
- 81 (3⁴)
- 256 (4⁴)
- 625 (5⁴)
- 1,296 (6⁴)
- 2,401 (7⁴)
- 4,096 (8⁴)
- 6,561 (9⁴)
- 10,000 (10⁴)
Fourth root vs. square root of a square root
The fourth root is mathematically equivalent to taking the square root twice. So ∜x = √(√x). For 256: √256 = 16, and √16 = 4, so ∜256 = 4.
