Square Root Calculator
Find the square root of any non-negative number, and check whether it is a perfect square.
How to use this calculator
- Enter any non-negative number.
- The result is the principal (positive) square root, to up to 8 decimal places.
The formula
√x = the number y such that y × y = x- x
- Any number ≥ 0
How it works
The square root reverses squaring. Because 12 × 12 = 144, √144 = 12.
Most numbers are not perfect squares; their roots are infinite non-repeating decimals that can only be approximated — this calculator rounds to 8 decimal places.
Worked example
Find √2 (the diagonal of a 1×1 square).
- 11² = 1 and 2² = 4, so the answer is between 1 and 2
- 21.414² = 1.999396 — close but low
- 3Refining further gives 1.41421356…
√2 ≈ 1.41421356.
When this calculator is useful
- Geometry — diagonals and the Pythagorean theorem
- Standard deviation in statistics
- Physics formulas (e.g. RMS values)
- Estimating distances
Frequently asked questions
Why can't I take the square root of a negative number?
No real number multiplied by itself is negative. Negative roots exist only in complex (imaginary) arithmetic, which this calculator does not perform.
Is √9 equal to 3 or −3?
The principal square root is 3. The equation x² = 9 has two solutions, 3 and −3, but the √ symbol denotes the positive one.