# Fourth Roots Calculator

## Calculator Use

Use this calculator to find the fourth root of a number. It accepts inputs of real numbers for the radicand. This online calculator is set up specifically to calculate 4th root. To calculate any root of a number use our Nth Root Calculator.

For complex or imaginary solutions use Simplify Radical Expressions Calculator.

## Fourth Roots

- Fourth root of 1 is ±1
- Fourth root of 16 is ±2
- Fourth root of 81 is ±3
- Fourth root of 256 is ±4
- Fourth root of 625 is ±5
- Fourth root of 1296 is ±6
- Fourth root of 2401 is ±7
- Fourth root of 4096 is ±8
- Fourth root of 6561 is ±9
- Fourth root of 10000 is ±10

## De Moivre's Theorem

for *k = 0, 1, ..., n-1*

## Fourth Root of a Negative Number

Find the fourth root of negative 81 with n=4 for the 4th root.

Solution:

Using DeMoivre's Theorem we get the equation

Solving our equation for k=0 to k=n-1 (for k = 0, 1, 2 and 3);

The roots of \( \sqrt[4]{-81} \) are:

### Further Reading

Dr Math The Fourth Root of -1

Dr Math DeMoivre's Theorem

De Moivre’s Theorem and Applications

**Cite this content, page or calculator as:**

Furey, Edward "Fourth Roots Calculator"; CalculatorSoup, *https://www.calculatorsoup.com* - Online Calculators