The Racine Carree Calculator evaluates square roots (√) for any real number you enter. The name comes from the French phrase racine carrée (square root), but the interface is in English for clarity. Results appear instantly with five-decimal precision, a simplified radical when possible, polar form, and step-by-step verification — including imaginary results for negative radicands.
Want a deeper walkthrough with examples? Read our Racine Carree Calculator guide for perfect squares, complex roots, and classroom tips.
How to use this calculator
- Enter a number in A = — type any positive value, decimal, or negative integer (default example: 25).
- Click Calculate — the √A preview and right-hand detail panel populate with your result.
- Review simplified form — perfect squares show integers; other values may show radicals like 5√2 or 9i for √−81.
- Check polar form — real roots display as magnitude ∠ 0°; pure imaginary roots use ∠ 90°.
- Reset or copy — Reset restores the default example; Copy Result places the principal value on your clipboard. Save downloads a text summary.
What is a square root?
A square root is a number that, when multiplied by itself, equals the original value. For example, √36 = 6 because 6 × 6 = 36. The radical symbol (√) denotes the operation; the number underneath is the radicand.
a = radicand, b = principal square root
Key concepts
- Radicand
- The value under √ — e.g. 25 in √25.
- Radical
- The √ symbol itself.
- Perfect square
- Integers such as 9, 16, or 49 with exact integer roots.
- Imaginary root
- When the radicand is negative, the principal root is complex — e.g. √−81 = 9i.
i = imaginary unit where i^2 = -1
Examples
Square root of a positive number
Enter 49 and the calculator returns 7 because √49 = 7. The steps panel verifies 7 × 7 ≈ 49.
Square root of a negative number
Enter −81 to get 9i. Mathematically, √−81 = √(81) × √(−1) = 9i. Polar form shows 9.000 ∠ 90°.
Why use the Racine Carree Calculator
- Accurate results — five-decimal precision without manual arithmetic.
- Instant output — click Calculate for immediate results with five-decimal precision.
- Advanced support — decimals, large numbers, perfect squares, and negative inputs.
- Educational breakdown — simplified radicals, polar notation, and verification steps for homework and study.
For related math tools, try our Percentage Calculator or Slope Calculator.