Root calculator (n-th root)

Root / n-th Root Calculator

This free root calculator allows you to find square roots, cube roots, and n-th roots of any number. Enter the number and the root degree (n) to get the result instantly.

Result will appear here.

Understanding Roots

An n-th root of a number x is a number r such that rⁿ = x. The most common roots are square roots (n=2) and cube roots (n=3).

Example: √16 = 4 because 4² = 16

Example: ∛27 = 3 because 3³ = 27

How the Calculator Works

The calculator automatically:

Step 1: Takes the number and root degree (n)

Step 2: Calculates the n-th root using JavaScript Math.pow(number, 1/n)

Step 3: Handles positive numbers and most fractional roots correctly

Step 4: Displays the result instantly

Examples

1. Square root: 25, n=2 → √25 = 5

2. Cube root: 27, n=3 → ∛27 = 3

3. Fourth root: 16, n=4 → 16^1/4 = 2

4. Fifth root: 32, n=5 → 32^1/5 = 2

Why Roots Matter

Roots are essential in algebra, geometry, physics, engineering, finance, and many real-world applications. They help solve equations, calculate measurements, and analyze data.

Common Mistakes to Avoid

- Forgetting that negative numbers cannot have even roots in real numbers.
- Confusing square roots with squares.
- Misinterpreting the root degree (n).

Important: Even roots of negative numbers are undefined in the real number system.

Correct: For odd roots (3,5,7…) negative numbers give a negative real result.

Frequently Asked Questions

Can the number be negative?

Yes, but only for odd roots. Even roots of negative numbers are undefined in real numbers.

Can the root degree be fractional?

Yes. Fractional roots represent powers. Example: x^(1/2) = √x

Does it round the result?

The calculator rounds results to 10 decimal places for readability.

Conclusion

Calculating n-th roots is a fundamental math skill. This root calculator provides quick and accurate results for any number and root degree, making math easier and error-free.