Root Calculator

Result
8
²√64

What Is a Root Calculator?

A root calculator finds the nth root of a number — the value that, when multiplied by itself n times, produces the original number. This includes square roots (n=2), cube roots (n=3), and any higher-degree root.

How to Use the Root Calculator

  1. Enter the number you want to find the root of.
  2. Enter the root degree (2 for square root, 3 for cube root, etc.).
  3. View the result instantly.

Root Formula

nth Root
ⁿ√x = x^(1/n)
n = the root degree
x = the number

Worked Examples

Example 1: Square Root of 64

√64 = 64^(1/2) = 8, since 8 × 8 = 64

Example 2: Cube Root of 27

³√27 = 27^(1/3) = 3, since 3 × 3 × 3 = 27

Understanding Your Results

For even-degree roots (like square roots) of negative numbers, there's no real number solution, since no real number multiplied by itself an even number of times produces a negative result — this calculator will indicate when a result is undefined for real numbers.

Common Uses for Roots

  • Geometry: finding side lengths from area (square root) or volume (cube root).
  • Statistics: standard deviation calculations use square roots.
  • Physics and engineering: many formulas involve roots (e.g., pendulum period, RMS calculations).

Common Mistakes to Avoid

  • Assuming every number has a real even-degree root — negative numbers don't have real square roots.
  • Confusing roots with exponents — they're inverse operations of each other.
  • Forgetting that a positive number technically has two square roots (positive and negative), though the "principal" root is the positive one shown by convention.

Frequently Asked Questions

Find the number that, when multiplied by itself, equals the original number. For example, the square root of 64 is 8, since 8×8=64.

Not as a real number — negative numbers don't have real square roots or other even-degree roots, since no real number multiplied by itself an even number of times gives a negative result.

The cube root of a number is the value that, when multiplied by itself three times, equals the original number. For example, the cube root of 27 is 3, since 3×3×3=27.

Roots are the inverse of exponents — the nth root of x is the same as x raised to the power of 1/n.

Yes — odd-degree roots (like cube roots) of negative numbers are defined and negative. For example, the cube root of −27 is −3.