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  4. Root Calculator

Root Calculator

Square, cube, and general nth-root calculator with principal root, ± for even roots, and verification.

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How it works

The nth root of a is b when bⁿ = a. Use square, cube, or general root modes. Real roots only.

ⁿ√a = b ⇔ bⁿ = a

When to use

Use this tool when you need to: pick Square, Cube, or General root. Even roots need a non-negative radicand; results show the principal root and ± when both are real.

How to use this tool

  1. Enter your values in the fields above.
  2. Review the formula and any mode options for your problem.
  3. Read the result and the step-by-step solution.

Pick Square, Cube, or General root. Even roots need a non-negative radicand; results show the principal root and ± when both are real.

Frequently asked questions

What is the Root Calculator?
The nth root of a is b when bⁿ = a. Use square, cube, or general root modes. Real roots only.
How do I use the Root Calculator?
Enter the required values, then calculate. The Root Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Root Calculator use?
ⁿ√a = b ⇔ bⁿ = a

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Square root calculator

Find the principal square root √x. Even roots need a non-negative radicand.

√
=
Result
?

Enter the number under the radical. For general roots, set the degree n first.

Try an example

How it works

What is a root?

The nth root of a number a is another number b such that b multiplied by itself n times equals a: ⁿ√a = b bⁿ = a Common cases are the square root (n = 2) and the cube root (n = 3). This calculator returns real roots only — even roots of negatives are not defined in the reals.

Estimating a square root

One hand method for √a: 1. Guess a number b 2. Divide a by b to get c 3. Average b and c for a better guess 4. Repeat until the desired precision Example: √27 to 3 decimals → about 5.196.

Estimating an nth root

For ⁿ√a, use a similar loop: guess b, compute c = a / bⁿ⁻¹, then replace the guess with [b×(n−1) + c] / n, and repeat. Example: eighth root of 15 ≈ 1.403 to three decimals.