The Fifth Root Calculator helps students, scientists, and engineers quickly find the fifth root of any number. Finding roots is common in math, physics, and engineering, especially when working with growth rates, scaling laws, and complex equations. Calculating a fifth root by hand can be slow, but this tool gives an instant answer with clear steps. This calculator belongs to the Mathematical Root and Exponent Calculator category and is widely used in education and research.
formula of Fifth Root Calculator
Fifth Root of a Number (x) = x^(1/5)
Where:
x is the number you want to find the fifth root of
1/5 is the exponent that means “fifth root”
This formula works for positive and negative numbers, but negative inputs may give complex results in some contexts.
Common Fifth Roots Reference Table
This table shows some typical fifth root values to help you check your answers or understand expected results.
| Number (x) | Fifth Root (x^(1/5)) |
|---|---|
| 1 | 1 |
| 32 | 2 |
| 243 | 3 |
| 1,024 | 4 |
| 3,125 | 5 |
| 10,000 | 6.31 |
| 100,000 | 10 |
This helps students spot patterns and verify manual calculations.
Example of Fifth Root Calculator
Let’s solve an example step by step.
Find the fifth root of 3,125.
- Use the formula:
Fifth Root = 3,125^(1/5) - You can rewrite this as:
3,125^(1/5) means “what number multiplied by itself five times equals 3,125?” - Try:
5 × 5 = 25
25 × 5 = 125
125 × 5 = 625
625 × 5 = 3,125
So, 5 is the fifth root.
Answer: 5
Most Common FAQs
A fifth root helps find a base value that, when raised to the fifth power, equals the original number. It is useful in scaling problems, polynomial equations, and scientific calculations.
Yes, but it depends. For odd roots like fifth roots, a real negative result exists. For example, the fifth root of −32 is −2. However, some calculators may show a complex number depending on settings.
A square root uses an exponent of 1/2 and finds a number that, when squared, gives the original value. A fifth root uses an exponent of 1/5 and finds a number that, when raised to the fifth power, equals the original number.