Fourth Root Calculator - Calculate ⁴√x
Result:
Welcome to our Fourth Root Calculator. This tool calculates the fourth root of any positive number, providing ⁴√x for any value of x you enter.
What is the Fourth Root?
The fourth root of a number x is a value that, when raised to the fourth power, gives x. ⁴√x = y means y⁴ = x
Understanding Fourth Roots
The fourth root is the inverse operation of raising a number to the fourth power:
- ⁴√16 = 2 because 2⁴ = 16
- ⁴√81 = 3 because 3⁴ = 81
- ⁴√1 = 1 because 1⁴ = 1
Perfect Fourth Powers
⁴√1 = 1
⁴√16 = 2
⁴√81 = 3
⁴√256 = 4
⁴√625 = 5
⁴√10000 = 10
Applications
Engineering: Fourth power scaling
Physics: Quartic relationships
Mathematics: Radical equations
Statistics: Fourth moment analysis
Computer Science: Algorithm complexity
Properties of Fourth Roots
- Domain: Only defined for non-negative real numbers
- Range: All non-negative real numbers
- Monotonic: If a > b ≥ 0, then ⁴√a > ⁴√b
- Even root: Principal root is always positive
Fourth Root Formula
⁴√x = x^(1/4)
Step-by-Step Calculation
Example: Find ⁴√256
Step 1: Identify the number
x = 256
Step 2: Apply the fourth root formula
⁴√256 = 256^(1/4)
Step 3: Calculate the result
256^(1/4) = 4
Verification: 4⁴ = 4 × 4 × 4 × 4 = 256 ✓
Common Fourth Roots
Perfect Fourth Power
⁴√625 = 5
5⁴ = 625Decimal Result
⁴√100 ≈ 3.162
Not a perfect fourth powerUnity
⁴√1 = 1
Any root of 1 equals 1Related Calculations
The fourth root is closely related to other mathematical operations:
- Square root of square root: ⁴√x = √(√x)
- Exponential form: ⁴√x = x^(0.25)
- Logarithmic relationship: log(⁴√x) = (1/4) × log(x)
- Inverse operation: (⁴√x)⁴ = x for x ≥ 0
Find Calculator
Popular Calculators
Other Calculators
