Fifth Root Calculator - Calculate ⁵√x
Result:
Welcome to our Fifth Root Calculator. This tool calculates the fifth root of any real number, providing ⁵√x for any value of x you enter.
What is the Fifth Root?
The fifth root of a number x is a value that, when raised to the fifth power, gives x. ⁵√x = y means y⁵ = x
Understanding Fifth Roots
The fifth root is the inverse operation of raising a number to the fifth power:
- ⁵√32 = 2 because 2⁵ = 32
- ⁵√-32 = -2 because (-2)⁵ = -32
- ⁵√1 = 1 because 1⁵ = 1
Perfect Fifth Powers
⁵√1 = 1
⁵√32 = 2
⁵√243 = 3
⁵√1024 = 4
⁵√3125 = 5
⁵√-32 = -2
Applications
Engineering: Fifth power scaling laws
Physics: Quintic relationships
Mathematics: Radical equations
Computer Science: Algorithm complexity
Statistics: Higher moment analysis
Properties of Fifth Roots
- Domain: All real numbers (positive and negative)
- Odd root: Preserves the sign of the input
- Monotonic: If a > b, then ⁵√a > ⁵√b
- Sign preservation: ⁵√(-x) = -⁵√x
Fifth Root Formula
⁵√x = x^(1/5)
Examples
Perfect Fifth Power
⁵√243 = 3
3⁵ = 243Negative Number
⁵√(-243) = -3
Odd root preserves signDecimal Result
⁵√100 ≈ 2.512
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