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Roots Calculator

Calculate nth roots with step-by-step working. Square roots, cube roots, and any root with precision control.

Root Results

ⁿ√x 0
Scientific Notation 0
Perfect Root Check -

Step-by-Step Calculation

How to Use the Roots 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. Adjust decimal places for precision (optional).
  4. Click "Calculate Root" to see the result.
  5. Review the step-by-step calculation and perfect root check.

Frequently Asked Questions

What is an nth root?

The nth root of a number x is a value that, when raised to the power n, equals x. For example, the square root (n=2) of 9 is 3 because 3² = 9. The cube root (n=3) of 8 is 2 because 2³ = 8.

What is a perfect root?

A perfect nth root occurs when a number is an exact integer raised to the power n. For example, 64 is a perfect square root because 8² = 64. 27 is a perfect cube root because 3³ = 27.

Can I take the root of a negative number?

Odd roots (cube root, 5th root, etc.) of negative numbers are real and negative. Even roots (square root, 4th root, etc.) of negative numbers result in complex (imaginary) numbers, which our calculator indicates.

How do I calculate roots manually?

For square roots, you can use estimation and refinement methods. For cube roots, you can use prime factorization if the number is a perfect cube. For general roots, use logarithms: ⁿ√x = x^(1/n) = e^((ln x)/n).

What is the relationship between roots and exponents?

Roots and exponents are inverse operations. If x = aⁿ, then a = ⁿ√x. The nth root can be calculated as x^(1/n). This relationship is fundamental in algebra and calculus.