Mathematics · Numbers and arithmetic
Calculate a square root (x ≥ 0)
Enter a number that is not negative. The tool returns the principal (nonnegative) square root. It is the inverse of squaring, not a cube root or an nth root.
Calculate
How the calculator works
The engine evaluates √x with JavaScript’s Math.sqrt. x < 0 is refused so the page never invents an imaginary part. √0 = 0. Display rounding does not change the identity y² ≈ x within floating-point noise.
Formula and method
√x = y with y ≥ 0 and y² = x
√9 = 3, not −3. Both 3 and −3 square to 9; this page reports the principal root only.
Principal square root on the nonnegative reals. Perfect squares of small integers come out exact in the display; most other inputs are irrational and are shown rounded. This is not a Pythagorean solver: if you have two legs, use that page, which applies √(a² + b²) for you.
Worked example
Perfect square
x = 81
- 9 × 9 = 81.
- Principal root 9.
√81 = 9.
Non-square
x = 2
- √2 is irrational.
- Display ≈ 1.414214 (your screen may show fewer digits).
√2 ≈ 1.414214. Squaring the display recovers 2 within rounding.
Input notes
- Value
- Radicand. Must be ≥ 0. 0 is allowed. Decimals are allowed (√6.25 = 2.5).
Assumptions and limits
Assumptions
- Real arithmetic, principal (nonnegative) root.
- Floating-point evaluation.
Limits
- No complex output for negative x.
- Not an nth-root calculator except n = 2 (use the exponent page for 1/3, with a ≥ 0).
How to read the result
If you need the side of a square of area 81, the side is 9. If you need both algebraic roots of y² = 81, they are 9 and −9; only 9 is printed here.
Common mistakes
Expecting √(a + b) = √a + √b.
Those are not equal. √(16 + 9) = 5, while 4 + 3 = 7.
Entering −9 and expecting 3i.
This page stays on the reals and rejects negatives.
Related calculations
- ExponentEvaluate aᵇ. Integers, decimals, negative exponents (reciprocals), and 1/2 (square root, base ≥ 0) are possible, within the reals and floating-point limits.
- Pythagorean theoremTwo modes: √(a² + b²) for the hypotenuse, or √(c² − a²) for the missing leg. The triangle must be right-angled; a “leg” longer than the hypotenuse is rejected.
- FractionsTwo integer fractions and an operation. The engine uses a common denominator or cross-products, then reduces by the GCF so the answer is in lowest terms.
- GCF (GCD)Enter at least two integers. The result is the largest positive integer that divides all of them — the same GCF used to reduce a fraction or a ratio.
- LCMEnter at least two nonzero integers. The result is the smallest positive integer that is a multiple of each — useful for common denominators and repeating schedules.
- RatioTwo integers in, a reduced ratio out (8 : 12 becomes 2 : 3), plus the quotient A/B and each term’s weight in the sum of absolute values — not “A as a percent of B.”
Frequently asked questions
Why isn’t −3 shown for √9?
The principal square root is defined to be ≥ 0.
The equation y² = 9 has two real solutions. The symbol √9 in this calculator means the nonnegative one. If you need ±, add the minus yourself.
Can I take the square root of a decimal?
Yes, if it is not negative.
√6.25 = 2.5 exactly. √2 will be a rounded irrational.
How do I get a hypotenuse from two sides?
Use the Pythagorean theorem page, or compute √(a² + b²) after squaring yourself.
This page only takes one radicand. The geometry tool applies a² + b² = c² and checks that lengths are positive.
Author and update
Written by Rédaction HexaCalc (editorial team). Content last updated: August 25, 2026. No third-party medical or financial review is claimed.
This calculation uses a standard mathematical identity. See also the methodology.
Right triangle next
If the square root is hiding inside a² + b² = c², let the Pythagorean tool form the radicand.
Open the Pythagorean calculatorCategory: Mathematics