Calculator tool
How this calculator works
Use the explanation to understand the formula, assumptions, and practical limits behind the calculator result.
What an nth root means
An th root asks which value raised to the power returns the original number:
The calculator returns the chosen root, plus the square root, cube root, and a quick verification line when the result is real.
Negative inputs need care
Odd roots of negative numbers stay real: the cube root of -8 is -2 because . Even roots of negative numbers are not real, so the calculator reports an imaginary value such as for the square root of -4. That distinction matters before you reuse the answer in a real-number formula.
Use the verification result to catch an incorrect degree or sign. If the verification raises the returned root back to a value close to the original input, the calculation is behaving as expected.
Frequently asked questions
What is the difference between a square root and an nth root?
A square root has degree 2. An nth root uses any positive integer degree you choose, such as 3 for cube root or 4 for fourth root.
Why are even roots of negative numbers imaginary?
Because squaring or using any even power on a real number cannot produce a negative result. Complex numbers are needed for those cases.
Why does the calculator show a verification line?
It raises the returned real root back to the chosen power so you can confirm it reproduces the original input approximately.
Can roots be irrational numbers?
Yes. For example, the square root of 2 cannot be written exactly as a finite decimal, so calculators show an approximation.
