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Square Root Calculator

Roots computed with IEEE-754 double precision (Math.sqrt, Math.cbrt). Radical form uses prime factorization — e.g. √72 = 6√2. Related: exponent, factor, Pythagorean theorem.

Square Root (√)
Cube Root (∛)
4th Root
Perfect Square
Prime Factorization
Simplified Radical Form
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Enter a number to see the worked formula.

What Your Result Means

How This Calculator Works

You enter any non-negative number. The tool computes square, cube, and fourth roots using JavaScript's built-in Math functions (IEEE-754 double precision). For the simplified radical, it runs a prime factorization, pairs up factors, pulls pairs outside the radical sign, and leaves the remainder under the root. Results are rounded to six decimal places.

Quick Questions

Can I find the square root of a negative number?

Not with real numbers — the square root of a negative number is imaginary. This calculator handles non-negative inputs only. For complex roots, the result would involve the imaginary unit i (e.g., √−4 = 2i).

What does "simplified radical form" mean?

It means rewriting a square root so no perfect-square factor remains under the radical. For example, √72 = √(36 × 2) = 6√2. This is the standard form expected in algebra and geometry classes.

Why does the calculator show 6 decimal places?

Six decimal places give enough precision for most practical and homework purposes while avoiding misleading extra digits. JavaScript's floating-point math is accurate to about 15–16 significant digits internally.

How is prime factorization related to square roots?

To simplify √n, you factor n into primes, group them in pairs, and move each pair outside the radical as a single factor. Unpaired primes stay inside. That's why 72 = 2³ × 3² simplifies to 6√2.

Sources

Method & review

MethodologyHow we calculate this Reviewed & Updated2026-04 Next review2027-04

Estimate only. Results reflect your inputs and standard formulas. Double-check important decisions independently.